Physical Constraints In physics, what does one mathematically mean by constraint in classical mechanics? What are the the different types/cases and how do people deal with them?
 A: A constraint along one or more directions means that some aspect of the motion of a body is prescribed along that direction(s). As a result, an unknown force must be applied along that direction to enforce the constraint.
Here are some rules about constraints


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*Any complex constraint dealing with multiple degrees of freedom can be decomposed into a sequence of simpler single degree of freedom constraints.

*Each simple constraint removes one degree of freedom from the system and adds an unknown reaction force (or torque).

*Constraint forces (or torques) do not add or remove energy to the system. This is precisely the definition of constraints as they don't allow any motion parallel to the reaction forces.

*Constraints can exist between a single body and the environment, or between two bodies. If between two bodies, the constraint forces are equal and opposite on the two bodies.

*Planar constraints are idealized with a relative center of rotation and constraint force line of action through the center of rotation.


In summary, if there is motion allowed along a particular direction then that direction cannot be part of a constraint. If the motion is restricted in any way, then a constraint exists and a corresponding force must be added to the free body diagram in order to make the problem solvable.
