sympy.physcis.mechanics // reaction force

[Peter Stahlecker]

When I use a velocity constraint to force a particle not to move in a certain direction, there must be a 'reaction force' on the particle.

I use KM.auxiliary_eqs to find reaction forces, which works very well in general!

However,  if I try to find the reaction force due to a velocity constraint, it does no seem to work:

The force term of the equations of motion contains the 'virtual speed', its time derivative and the reaction force.

Am I doing something wrong, or do velocity_constraints and KM.auxiliary_eqs just not work together?

I attach some code, showing my problem.

Any help is greatly appreciated!

[Jason Moore]

The virtual speeds will appear in the force equations, but you then just set them to zero because they are fictitious. You force equation should then be correct.

Jason

moorepants.info
+01 530-601-9791

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[Peter Stahlecker]

Thanks! Would I also set the 'reaction forces' appearing in the force term equal to zero?

As per my understanding of mechanics, they also should have no influence on the equations of motion (?)

[Jason Moore]

Peter,

If you have a particle that is forced to move along a path (typically be a configuration constraint), then there exists reaction forces normal to the path that keep it on the path. These forces are not present in the equations of motion when they are formed with minimal coordinates. But you can expose the forces by introducing fictitious (auxiliary) generalized speeds normal to the path and a variable for the forces. This will result in the minimal equations of motion and some algebraic equations for the forces. All of these equations will have the aux speeds, which then must be set to zero because they are fictitious. This should then leave you with the equations of motion plus some equations that can be solved for the forces.

Jason

moorepants.info
+01 530-601-9791

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[Peter Stahlecker]

Dear Jason,

Thanks!

If I understood correctly, if I use velocity constraints, I do not use the minimal number of generalized coordinates, hence these reaction forces and 'virtual' speeds appear in my force term of the equations of motion. As they are normal to the motion of the particle(s), I simply set them to zero in the force term.

Peter

[Jason Moore]

Peter,

Yes, the velocity constraints work the same way. There are reaction forces that constrain the velocities.

Jason

moorepants.info
+01 530-601-9791

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[Peter Stahlecker]

Dear Jason,

Now all clear to me, thanks!

Peter

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