4
votes
2answers
526 views

Is there any case in physics where the equations of motion depend on high time derivatives of the position?

For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order ...
6
votes
2answers
1k views

Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
0
votes
1answer
439 views

Laws of Motion: Acceleration to be applied on a free falling object to reduce velocity to 0

Assume that an object of mass 'm' is falling to the earth.The force acting on the same would be F = m*g = 10m (assuming g = 10m/s^2). In this case the velocity of the object at time 't' = 10 seconds ...