Generalized coordinates and generalized forces

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Any number of possibilities exist for the choice of generalized coordinates to be used for a given problem. As mentioned earlier in the lecture, we need to guarantee that the choice of coordinates completely describe the position/orientation of each body and that the coordinates be independent.

Consider the following system made up of three bodies: Bodies 1 and 3 (each constrained to move along a smooth horizontal surface) and Body 2 (having a length of L, pinned to Body 1 and constrained to move in smooth vertical slot in Body 3). A horizontal force F acts to the right on Body 3.

 The following represent SOME of the possible generalized coordinates that can be used to describe the motion of the system:

 

Generalized coordinates Set No. 1:

 

Generalized coordinates Set No. 2:

 

Generalized coordinates Set No. 3:

 EXERCISE:
Verify that the above three sets of coordinates satisfy the requirements of being generalized coordinates. Also, determine the inertia coordinates and generalized forces for each set of generalized coordinates. What is the physical interpretation of the generalized forces (force or moment) in each case?