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Puzzle 4
- Thread starter zekeman
- Start date
btrueblood
Mechanical
"So you are saying that a rope attached to the bob can sustain a horizontal component of force at the pivot point.
Think again. The only forces on the rope are tensile."
Right. But if the rope is inclined at some angle to vertical, what are the reactions relative to horizontal? If no horizontal forces can be generated at the pivot point, then the swing will never swing, and any push given the rider will just send him sailing away over the horizon (this un-restrained swing is the equivalent of a guy on a frictionless surface). There are no forces reacted by the rope at the bottom of the arc of the swing - in this you are correct. But it is exactly that imbalance of forces that causes the center of mass to shift out-of-perpendicular, and thus start the oscillation of the swing.
"My take is that in a vacuum with and without friction there is no net reaction force and no starting the swing."
...
IF the kid can change the location of his c.o.m., then the swing will move, right?
When the kid's muscles contract, he accelerates the c.o.m. of his legs, and the muscles/bones react that (acceleration x mass = force) against what - the c.o.m. of the rest of his body. That force acts for a very short period relative to the natural frequency of the pendulum, but nevertheless, the integral of force over time generates a small displacement of the center of mass of the system. Granted, the displacement generated is small, and he has to repeatedly pump those legs at both the proper frequency and the proper phase in order to increase the amplitude of the swing over time, but friction need not be invoked to generate the forces and displacements.
You can talk about his arms bending the rope, and that technique works too for the same reasons as just moving his legs (he is shifting his weight about the pivot created by his hands holding the rope, thus shifting his c.o.m.).
There is a type of swing used by circus performers that has a long platform in place of the swing seat, and rigid links to the pivot points. You can watch a performer start from the swing perfectly at rest, and he then begins to shift his body (running, leaping, and stopping, then reversing direction) from one end of the platform to the next, eventually pumping the swing enough to go over-the-top (loop the loop).
But I'm coming to a point where I agree with rb1957.
Think again. The only forces on the rope are tensile."
Right. But if the rope is inclined at some angle to vertical, what are the reactions relative to horizontal? If no horizontal forces can be generated at the pivot point, then the swing will never swing, and any push given the rider will just send him sailing away over the horizon (this un-restrained swing is the equivalent of a guy on a frictionless surface). There are no forces reacted by the rope at the bottom of the arc of the swing - in this you are correct. But it is exactly that imbalance of forces that causes the center of mass to shift out-of-perpendicular, and thus start the oscillation of the swing.
"My take is that in a vacuum with and without friction there is no net reaction force and no starting the swing."
...
IF the kid can change the location of his c.o.m., then the swing will move, right?
When the kid's muscles contract, he accelerates the c.o.m. of his legs, and the muscles/bones react that (acceleration x mass = force) against what - the c.o.m. of the rest of his body. That force acts for a very short period relative to the natural frequency of the pendulum, but nevertheless, the integral of force over time generates a small displacement of the center of mass of the system. Granted, the displacement generated is small, and he has to repeatedly pump those legs at both the proper frequency and the proper phase in order to increase the amplitude of the swing over time, but friction need not be invoked to generate the forces and displacements.
You can talk about his arms bending the rope, and that technique works too for the same reasons as just moving his legs (he is shifting his weight about the pivot created by his hands holding the rope, thus shifting his c.o.m.).
There is a type of swing used by circus performers that has a long platform in place of the swing seat, and rigid links to the pivot points. You can watch a performer start from the swing perfectly at rest, and he then begins to shift his body (running, leaping, and stopping, then reversing direction) from one end of the platform to the next, eventually pumping the swing enough to go over-the-top (loop the loop).
But I'm coming to a point where I agree with rb1957.
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2
- #102
Wrenchbender
Mechanical
The swinger supplies (biological) energy to the system by changing their CG. Journal papers have already been published on this topic. Search 'pumping a playground swing'. Some hits include:
GregLocock
Automotive
Sounds like we all hit on the same solution - the swingers arms are a very important part of the system, if you have a chain, and the time constants of the compound pendulum matter.
Call the top pivot H1, and the point where the arms hold onto the chain H2.
create a swing seat hanging below H2, CG obviously directly below h1 and H2. This has a high moment of inertia.
Now add a mass on a horizontal slider initially under H2.
Slowly move the mass away, the seat tips up, and the CG of the seat+mass, H2 and H1 remain colinear. No oscillation.
OK, that's the statics.
Now reset the mechanism, and this time move the mass very quickly.
The seat moves in the opposite direction, horizontally, as before, but due to its large MoI does not rotate, so H2 moves in the same direction. The chain, h1 to h2 is now off the vertical and the tension in it applies a torque about the CG of the seat mass system, which slowly rotates to bring H1 and H2 and the CG colinear, and then overshoots, and just sits there jiggling around the static location. Note that work was done on the first motion of the mass, this is what supplies the initial rotational kinetic energy of the seat/mass system. Once there is an oscillation then the mass can be moved in such a way as to feed more energy into the system.
So, that works. Is it how a real child gets a swing moving? No probably not. Swinging your legs is a far more obvious way of setting up a rotational motion. However it is robust (it needed no fine tuning to get it to work), obeys the laws of physics, doesn't rely on friction, and works equally well with chains or rigid links.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
Call the top pivot H1, and the point where the arms hold onto the chain H2.
create a swing seat hanging below H2, CG obviously directly below h1 and H2. This has a high moment of inertia.
Now add a mass on a horizontal slider initially under H2.
Slowly move the mass away, the seat tips up, and the CG of the seat+mass, H2 and H1 remain colinear. No oscillation.
OK, that's the statics.
Now reset the mechanism, and this time move the mass very quickly.
The seat moves in the opposite direction, horizontally, as before, but due to its large MoI does not rotate, so H2 moves in the same direction. The chain, h1 to h2 is now off the vertical and the tension in it applies a torque about the CG of the seat mass system, which slowly rotates to bring H1 and H2 and the CG colinear, and then overshoots, and just sits there jiggling around the static location. Note that work was done on the first motion of the mass, this is what supplies the initial rotational kinetic energy of the seat/mass system. Once there is an oscillation then the mass can be moved in such a way as to feed more energy into the system.
So, that works. Is it how a real child gets a swing moving? No probably not. Swinging your legs is a far more obvious way of setting up a rotational motion. However it is robust (it needed no fine tuning to get it to work), obeys the laws of physics, doesn't rely on friction, and works equally well with chains or rigid links.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
rb1957 - may I suggest you read and think about what people actually say, rather than what you think they are saying.
There is no point in looking at how kids actually go about swinging because no-one disputes that a swing motion can be amplified by moving the centre of mass relative to the pivot point, once there is some movement, or the centre of mass has some accelleration. The question is, where does the initial accelleration come from in a system starting from rest with the centre of rest exactly under the pivot?
The answer is not is not that a rapid movement of the legs will cause the centre of mass of the system to move, even momentarily. It will not. If there is no external horizontal force the centre of mass stays precisely where it is horizontally. Certainly you can move the centre of mass vertically along the line of the rope, but that won't generate any horizontal force.
The answer is that although you can't move the centre of mass horizontally starting from rest, you can move the position of a point on the rope relative to the pivot (and the centre of mass). This position is unstable, and rotation of the body will tend to bring the two points back into line, but it does provide a temporary horizontal force (the horizontal component of the tension in the rope), which will accellerate the centre of mass, and this accelleration can then be amplified as discussd at length earlier in the thread.
Maybe you think this is a pedantic point, but I think it is important to recognise that if you have a system with no external force in a given direction nothing you do will accellerate the centre of mass in that direction, even momentarily, unless and until some external force is applied.
Doug Jenkins
Interactive Design Services
There is no point in looking at how kids actually go about swinging because no-one disputes that a swing motion can be amplified by moving the centre of mass relative to the pivot point, once there is some movement, or the centre of mass has some accelleration. The question is, where does the initial accelleration come from in a system starting from rest with the centre of rest exactly under the pivot?
The answer is not is not that a rapid movement of the legs will cause the centre of mass of the system to move, even momentarily. It will not. If there is no external horizontal force the centre of mass stays precisely where it is horizontally. Certainly you can move the centre of mass vertically along the line of the rope, but that won't generate any horizontal force.
The answer is that although you can't move the centre of mass horizontally starting from rest, you can move the position of a point on the rope relative to the pivot (and the centre of mass). This position is unstable, and rotation of the body will tend to bring the two points back into line, but it does provide a temporary horizontal force (the horizontal component of the tension in the rope), which will accellerate the centre of mass, and this accelleration can then be amplified as discussd at length earlier in the thread.
Maybe you think this is a pedantic point, but I think it is important to recognise that if you have a system with no external force in a given direction nothing you do will accellerate the centre of mass in that direction, even momentarily, unless and until some external force is applied.
Doug Jenkins
Interactive Design Services
The concluding line in the above post just proved Newtons third law. ![[smarty]](/data/assets/smilies/smarty.gif "[smarty] [smarty]")
. The circle is closed.... just kidding. ![[smile]](/data/assets/smilies/smile.gif "[smile] [smile]")
I did not finish my problem I started earlier. Although what Greg described is almost exactly what I did, except he finished the thought, that I did not.
![[peace]](/data/assets/smilies/peace.gif "[peace] [peace]")
Fe
. The circle is closed.... just kidding. I did not finish my problem I started earlier. Although what Greg described is almost exactly what I did, except he finished the thought, that I did not.
Fe
btrueblood
Mechanical
IDS - "read and think about what people actually say, rather than what you think they are saying."
I absolutely agree with you.
Which is why I'm gonna give Greg a star.
I absolutely agree with you.
Which is why I'm gonna give Greg a star.
Compositepro
Chemical
I don't think Greg's explanation is correct. I now believe that you cannot start the swing from a motionless state with no external forces. All forces have equal and opposite reactions. The COM will always be under the pivot point and cannot move from there without external force. Bending the rope from vertical does nothing. The rope only has tensile forces and the COM is still exactly under the pivot. So no net torque about the pivot.
Greg's link explained how swings work but did not address what we are discussing. What I learned from it though is that it is the shift in mass to and from the pivot point during the swing that pumps it. This works only when there is already a swinging motion.It cannot start a swing. The COM cannot be moved tangentially to the swing of the rope without an external force. The rider can only move his COM along the axis of the rope by swinging the legs or by standing and squatting on the seat. But this cannot start the swing.
Greg's link explained how swings work but did not address what we are discussing. What I learned from it though is that it is the shift in mass to and from the pivot point during the swing that pumps it. This works only when there is already a swinging motion.It cannot start a swing. The COM cannot be moved tangentially to the swing of the rope without an external force. The rider can only move his COM along the axis of the rope by swinging the legs or by standing and squatting on the seat. But this cannot start the swing.
ChrisDuncan
Mechanical
Compositepro,
read the links in Bestwrench's post. The force is internal. It starts from rest when you move the small pendulum from the pivot where you grab the rope. You swing your legs back and forth and they gain angular momentum. Through timing and phase this is transferred to the larger pendulum and increased by either "parametric oscillation" (spinning skater centralizing mass) or "driven oscillation", moving back at the peak of back swing and forward at peak of forward swing, which increases the distance of oscillation.
I think the reason it's so hard to start the swing is that when you transfer the angular momentum from the short pendulum to the long pendulum in increases the moment of inertia by the multiple distance of long pendulum over short. Thus slowing the rotation rate by that multiple.
I'm just wondering what the kids are going to think when I tell them we're going to the park to play on the double pendulum mechanism and see if we can test the conservation of angular momentum through parametric oscillation.
read the links in Bestwrench's post. The force is internal. It starts from rest when you move the small pendulum from the pivot where you grab the rope. You swing your legs back and forth and they gain angular momentum. Through timing and phase this is transferred to the larger pendulum and increased by either "parametric oscillation" (spinning skater centralizing mass) or "driven oscillation", moving back at the peak of back swing and forward at peak of forward swing, which increases the distance of oscillation.
I think the reason it's so hard to start the swing is that when you transfer the angular momentum from the short pendulum to the long pendulum in increases the moment of inertia by the multiple distance of long pendulum over short. Thus slowing the rotation rate by that multiple.
I'm just wondering what the kids are going to think when I tell them we're going to the park to play on the double pendulum mechanism and see if we can test the conservation of angular momentum through parametric oscillation.
- Thread starter
- #109
Bestwrench,
Those are great videos
None show any static start.
My take on the dynamics is seen from the first video where the key is the bob rising up the rope near the end of travel, thus reducing the length, r and since angular momentum is conserved (m*v*r= constant), then v increases as r decreases; the increase of v is due to the work done in climbing up the rope near the end of the travel, so we have an increase in energy, v and when the bob returns to the center position we have a higher velocity than it had previously; this process ,repeated, will cause sustained oscillation growing until perhaps friction or running out of height limits it.
The kid pumping his feet essentially mimics that motion since raising the feet causes the CM to rise
Those are great videos
None show any static start.
My take on the dynamics is seen from the first video where the key is the bob rising up the rope near the end of travel, thus reducing the length, r and since angular momentum is conserved (m*v*r= constant), then v increases as r decreases; the increase of v is due to the work done in climbing up the rope near the end of the travel, so we have an increase in energy, v and when the bob returns to the center position we have a higher velocity than it had previously; this process ,repeated, will cause sustained oscillation growing until perhaps friction or running out of height limits it.
The kid pumping his feet essentially mimics that motion since raising the feet causes the CM to rise
ChrisDuncan
Mechanical
If you can add force once in motion, without anything to push off of, why can't you add force from a standing start?
The key difference is not the motion, it is the inclination of the rope or rod. If you have an inclined rope you do have something to push off (or in the case of a rope, pull on). When the swing is in motion then the rope is inclined (except momentarilly at the bottom of the swing). When it is not in motion then it is necessary to get some inclination in the rope, and that can be done by moving some part of the rope relative to the centre of mass.
Doug Jenkins
Interactive Design Services
btrueblood
Mechanical
"I now believe that you cannot start the swing from a motionless state with no external forces. "
There are two external forces. Gravity is one. The fixed pivot (the rope tied to the tree branch) is the second. This is not a free system, but a grounded system, with the grounding occurring at two seperated (but connected, via the swing ropes) points.
A star for tygerdawg, who made a good stab way up there ^ at a text description of the ideas. A star for Bestwrench, although you need a subscription to read either of his two references. Greg already has his star both for his model and for his paper reference.
Better are these, which describe the phenomena in (exhaustive!) detail, including stepwise derivation of the equations, and :
Please read the conclusion of the second paper at least, where it notes that the angular motion of the seated rider has an additive effect to the amplitude of swing motion, independent of the swing's amplitude (i.e. even if the initial angle of the swing is zero). This is shown in the plots in Greg's reference, but the explicit statement of the initial conditions is not made. They do also mention that their analysis assumes rigid links, not ropes. But I can show at least two ways where that wouldn't matter (one: the kid is a rigid link between the mass of his lardy butt and his legs). Both papers describe, and the first one graphs, how the driven angular oscillation motion of the suspended barbell (simulating the rider) can force oscillations of the entire swing, even from (please see the detailed description in the first paper) initial conditions with upper swing angle at zero, and first derivative of upper angle w.r.t. time of zero.
It is interesting that angular momentum is conserved, and in fact is essential (the transfer of that momentum from the lower oscillating system to the upper or global system is the mechanism at work), but - energy is clearly not conserved, as the energy in the system (provided by the suspended forcing function, i.e. rider) grows over time.
The best example of conservation of angular momentum does not mean that rotations of a multiple-jointed body cannot occur:
(ok, that was just for fun
Whoops - nope, on third reading, Greg's paper does state (p. 465, bottom right) "When started from rest, the swing's amplitude will grow linearly...". Presumably, "at rest" means no initial motion, which also implies an initial angle of zero.
The stake has been well and fully driven into this one, the horse is long dead.
There are two external forces. Gravity is one. The fixed pivot (the rope tied to the tree branch) is the second. This is not a free system, but a grounded system, with the grounding occurring at two seperated (but connected, via the swing ropes) points.
A star for tygerdawg, who made a good stab way up there ^ at a text description of the ideas. A star for Bestwrench, although you need a subscription to read either of his two references. Greg already has his star both for his model and for his paper reference.
Better are these, which describe the phenomena in (exhaustive!) detail, including stepwise derivation of the equations, and :
Please read the conclusion of the second paper at least, where it notes that the angular motion of the seated rider has an additive effect to the amplitude of swing motion, independent of the swing's amplitude (i.e. even if the initial angle of the swing is zero). This is shown in the plots in Greg's reference, but the explicit statement of the initial conditions is not made. They do also mention that their analysis assumes rigid links, not ropes. But I can show at least two ways where that wouldn't matter (one: the kid is a rigid link between the mass of his lardy butt and his legs). Both papers describe, and the first one graphs, how the driven angular oscillation motion of the suspended barbell (simulating the rider) can force oscillations of the entire swing, even from (please see the detailed description in the first paper) initial conditions with upper swing angle at zero, and first derivative of upper angle w.r.t. time of zero.
It is interesting that angular momentum is conserved, and in fact is essential (the transfer of that momentum from the lower oscillating system to the upper or global system is the mechanism at work), but - energy is clearly not conserved, as the energy in the system (provided by the suspended forcing function, i.e. rider) grows over time.
The best example of conservation of angular momentum does not mean that rotations of a multiple-jointed body cannot occur:
(ok, that was just for fun
Whoops - nope, on third reading, Greg's paper does state (p. 465, bottom right) "When started from rest, the swing's amplitude will grow linearly...". Presumably, "at rest" means no initial motion, which also implies an initial angle of zero.
The stake has been well and fully driven into this one, the horse is long dead.
When the kid bends the rope applying an horizontal force on it, an angle is created and two tensile forces arise on the rope (one acting on the part of rope form the pivot point to the point where the kid applies the horizontal force and one acting on the part of the rope from the bob to the the point where the kid applies the horizontal force). The start position, which represents a stable equilibrium position (as per Lyapunov stability theorem), is perturbed and so the system tries to recover it.
GregLocock
Automotive
Some plots of the system I described. To my mind fast_step raises as many questions as it answers. I really like the phaseplane plot on increasing_sine.
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
Cheers
Greg Locock
I rarely exceed 1.79 x 10^12 furlongs per fortnight
SomptingGuy
Automotive
Hmmm, I wonder if my daughter realises we're going to the park at the weekend?
- Steve
- Steve
- Thread starter
- #116
I read the second reference given by Trueblood(TB) and looked at
Bestwrench(BR) model videos.
The guy stands up at the peak of the swing in BR model and sits at the o position which is opposite to TB's guy.
It is obvious to me that it does not matter where in the cycle you stand up, and sit down you will get amplification.
Standing up increases the the total energy of the system,since work is done against gravity, while sitting down will not remove all of that energy.
Just think during sitting down at the end of the stroke you suddenly drop your body most of the energy increment is preserved; although, dropping the body at the 0 angle position may lose some energy through tension in the rope.
So, both models make the clear case that by standing you increase the total energy and dropping to the sitting position hardly changes the total energy, you have increasing velocity at the 0 position for each cycle with increasing amplitude.
I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope.
Bestwrench(BR) model videos.
The guy stands up at the peak of the swing in BR model and sits at the o position which is opposite to TB's guy.
It is obvious to me that it does not matter where in the cycle you stand up, and sit down you will get amplification.
Standing up increases the the total energy of the system,since work is done against gravity, while sitting down will not remove all of that energy.
Just think during sitting down at the end of the stroke you suddenly drop your body most of the energy increment is preserved; although, dropping the body at the 0 angle position may lose some energy through tension in the rope.
So, both models make the clear case that by standing you increase the total energy and dropping to the sitting position hardly changes the total energy, you have increasing velocity at the 0 position for each cycle with increasing amplitude.
I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope.
Boy! All that stuff about rigid members, I can't wait for the next thread on gyroscopes.
JMW
JMW
btrueblood
Mechanical
Forget the standing/sitting method, the first author admits that method won't start a stationary swing (there is no lateral displacment of mass). Focus on the rotating, seated swinger.
"I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope."
Their comment is regarding the idea that the perfect pin joint at the seat (junction of upper swing rope/link to the center of the dumbell) cannot support a torque, if the upper member is a rope (ropes don't support moments).
But, if a kid grabs the rope above the pivot, he creates a second rigid link between his arms and torso, which can create moments relative to other parts of his body. I.e. the system modelled in the references would add one more link and rigid member. This has been said by others, but it may be difficult to visualize.
Let's simplify it by re-sketching the first paper's "Figure 1", see the attached sketch Figure "A". Of course, I've now invoked a third link and third angle to the system...
After it's all said and done, think about the mathematical ideal of a massless rope with zero moment of inertia...ok, maybe it can't be started from rest...I can draw the free body diagram for such a case (figure B1 thru B3), and (I think) argue convincingly that the upper link cannot be displaced relative to the fixed pivot unless the rope has inertia...
So, ok, I will allow the hypotheses that a swing suspended from massless rope might not start from a rest position...please send me some of that rope so we can prove the theory.
"I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope."
Their comment is regarding the idea that the perfect pin joint at the seat (junction of upper swing rope/link to the center of the dumbell) cannot support a torque, if the upper member is a rope (ropes don't support moments).
But, if a kid grabs the rope above the pivot, he creates a second rigid link between his arms and torso, which can create moments relative to other parts of his body. I.e. the system modelled in the references would add one more link and rigid member. This has been said by others, but it may be difficult to visualize.
Let's simplify it by re-sketching the first paper's "Figure 1", see the attached sketch Figure "A". Of course, I've now invoked a third link and third angle to the system...
After it's all said and done, think about the mathematical ideal of a massless rope with zero moment of inertia...ok, maybe it can't be started from rest...I can draw the free body diagram for such a case (figure B1 thru B3), and (I think) argue convincingly that the upper link cannot be displaced relative to the fixed pivot unless the rope has inertia...
So, ok, I will allow the hypotheses that a swing suspended from massless rope might not start from a rest position...please send me some of that rope so we can prove the theory.
- Thread starter
- #119
"Forget the standing/sitting method, the first author admits that method won't start a stationary swing (there is no lateral displacment of mass). Focus on the rotating, seated swinger."
< why forget him. I was referring to him>
"I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope."
> my quote from that authors comment>
"Their comment is regarding the idea that the perfect pin joint at the seat (junction of upper swing rope/link to the center of the dumbell) cannot support a torque, if the upper member is a rope (ropes don't support moments).'
>A perfect pin has nothing to do with a rod that replaces an ideal rope>
"But, if a kid grabs the rope above the pivot, he creates a second rigid link between his arms and torso, which can create moments relative to other parts of his body. I.e. the system modelled in the references would add one more link and rigid member. This has been said by others, but it may be difficult to visualize."
> why add a another complication to an already complicated system. And, moreover, by adding another link you are still left with the rope above his hand where I suppose you get another ideal pivot, but what is the point>
Let's simplify it by re-sketching the first paper's "Figure 1", see the attached sketch Figure "A". Of course, I've now invoked a third link and third angle to the system...
"After it's all said and done, think about the mathematical ideal of a massless rope with zero moment of inertia...ok, maybe it can't be started from rest...I can draw the free body diagram for such a case (figure B1 thru B3), and (I think) argue convincingly that the upper link cannot be displaced relative to the fixed pivot unless the rope has inertia..."
> Those are the strangest free body diagrams I have ever seen.I don't have a clue.
Also you say an inertialess rope won't support the "model" or the physics; which is it?
"So, ok, I will allow the hypotheses that a swing suspended from massless rope might not start from a rest position...please send me some of that rope so we can prove the theory"
> Look in your neighbor's backyard.You don't really think its a rod or it has weight significant enough to change a well developed model. The models that do not allow for a flexible rope are somewhat.>
I do appreciate the math models and remember the solution is
often limited by the assumptions made.
I have looked at the standing- sitting method and am satisfied that the amplitude grows ( assuming a finite starting energy)since every time the guy stands he adds energy to the system, and there is no easy way to remove it (eg sitting down)
If you carry that out for the kid pumping, even without raising his CM, then there is a valid case that the energy of pumping (1/2Iw^2),will eventually manifest itself into increasing the energy of the system, and thus increase the amplitude.
So I believe that you don't need the math to understand this phenomenon.
I now firmly believe that any method of increasing the energy of the system,standing or thrashing will increase the velocity at the 0 position and thus increase the amplitude. Absent friction it will runaway.
Prove this wrong.
*
< why forget him. I was referring to him>
"I'm totally puzzled by the conclusion of TB's authors who limited the analysis to a rod rather than an ideal rope."
> my quote from that authors comment>
"Their comment is regarding the idea that the perfect pin joint at the seat (junction of upper swing rope/link to the center of the dumbell) cannot support a torque, if the upper member is a rope (ropes don't support moments).'
>A perfect pin has nothing to do with a rod that replaces an ideal rope>
"But, if a kid grabs the rope above the pivot, he creates a second rigid link between his arms and torso, which can create moments relative to other parts of his body. I.e. the system modelled in the references would add one more link and rigid member. This has been said by others, but it may be difficult to visualize."
> why add a another complication to an already complicated system. And, moreover, by adding another link you are still left with the rope above his hand where I suppose you get another ideal pivot, but what is the point>
Let's simplify it by re-sketching the first paper's "Figure 1", see the attached sketch Figure "A". Of course, I've now invoked a third link and third angle to the system...
"After it's all said and done, think about the mathematical ideal of a massless rope with zero moment of inertia...ok, maybe it can't be started from rest...I can draw the free body diagram for such a case (figure B1 thru B3), and (I think) argue convincingly that the upper link cannot be displaced relative to the fixed pivot unless the rope has inertia..."
> Those are the strangest free body diagrams I have ever seen.I don't have a clue.
Also you say an inertialess rope won't support the "model" or the physics; which is it?
"So, ok, I will allow the hypotheses that a swing suspended from massless rope might not start from a rest position...please send me some of that rope so we can prove the theory"
> Look in your neighbor's backyard.You don't really think its a rod or it has weight significant enough to change a well developed model. The models that do not allow for a flexible rope are somewhat.>
I do appreciate the math models and remember the solution is
often limited by the assumptions made.
I have looked at the standing- sitting method and am satisfied that the amplitude grows ( assuming a finite starting energy)since every time the guy stands he adds energy to the system, and there is no easy way to remove it (eg sitting down)
If you carry that out for the kid pumping, even without raising his CM, then there is a valid case that the energy of pumping (1/2Iw^2),will eventually manifest itself into increasing the energy of the system, and thus increase the amplitude.
So I believe that you don't need the math to understand this phenomenon.
I now firmly believe that any method of increasing the energy of the system,standing or thrashing will increase the velocity at the 0 position and thus increase the amplitude. Absent friction it will runaway.
Prove this wrong.
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You need to focus on change of momentum, not change of energy.
You can jump up and down all you like, if your centre of mass is exactly below the pivot point (which it will be if you start from rest) and the rope is vertical, you won't move anywhere. You will just convert a lot of chemical energy into potential energy, and then into kinetic energy, and then into heat.
Starting from rest you need to displace the rope horizontally at some point, and you can do that by pushing another part of the rope in the opposite direction. Once there is even a small deviation from the vertical you have a source of a horizontal reaction, and can start to move your centre of mass in the horizontal direction.
Doug Jenkins
Interactive Design Services
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