- #1
boeing_737
- 12
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Hi all,
I am having trouble understanding Virtual displacements and related ideas and would appreciate your help!
Let's say we have a simple pendulum and we take a snapshot of this system at some instant of time :
A 'virtual displacement' is said to be :
- consistent with the constraints on the system
- occurs without the passage of time
- is infinitesimal
In the case above, the mass can undergo a virtual displacement along the pink dotted line, since any other displacement would cause the string/rod to elongate, thus violating the constraint. Also, the virtual displacement along the pink dotted line has to be infinitesimal as a large virtual displacement would cause a change in the length of the string/rod. The forces acting at this instant on the mass are the weight and the reaction force/tension. It would seem that the reaction force, which is the force maintaining the constraint is perpendicular to the virtual displacement and hence would do no 'virtual work'. But why is it important that the no time elapse during this displacement? Is it because the external and constraint forces may change directions and (possibly) magnitudes?
Also, real displacements obey the system constraints (the mass moves in an arc). So apart from the idea that virtual displacements occur without time elapsing, what is the difference between the two?
Finally, what I find really puzzling is that the principle of virtual work is an important step in deriving Lagrange's equation. How is it that some relations that are based on imaginary displacements give rise to equations relating physical quantities?
Am I missing something here? Any help would be greatly welcomed. :)
Thanks,
yogesh
I am having trouble understanding Virtual displacements and related ideas and would appreciate your help!
Let's say we have a simple pendulum and we take a snapshot of this system at some instant of time :
A 'virtual displacement' is said to be :
- consistent with the constraints on the system
- occurs without the passage of time
- is infinitesimal
In the case above, the mass can undergo a virtual displacement along the pink dotted line, since any other displacement would cause the string/rod to elongate, thus violating the constraint. Also, the virtual displacement along the pink dotted line has to be infinitesimal as a large virtual displacement would cause a change in the length of the string/rod. The forces acting at this instant on the mass are the weight and the reaction force/tension. It would seem that the reaction force, which is the force maintaining the constraint is perpendicular to the virtual displacement and hence would do no 'virtual work'. But why is it important that the no time elapse during this displacement? Is it because the external and constraint forces may change directions and (possibly) magnitudes?
Also, real displacements obey the system constraints (the mass moves in an arc). So apart from the idea that virtual displacements occur without time elapsing, what is the difference between the two?
Finally, what I find really puzzling is that the principle of virtual work is an important step in deriving Lagrange's equation. How is it that some relations that are based on imaginary displacements give rise to equations relating physical quantities?
Am I missing something here? Any help would be greatly welcomed. :)
Thanks,
yogesh