In our treatment of systems of n particles we have, in general, considered the configuration to be fixed by 3n = N Cartesian coordinates in configuration space. If the system is constrained by equality constraints we conclude that these constraints define either surfaces or elements of tangent planes to surfaces, and the point defining the configuration in the configuration space (or the point defining the state in state space) must lie in these surfaces. To mention a concrete example, a simple spherical pendulum consists of a particle that moves on the surface of a sphere. Therefore, three Cartesian coordinates define its position, but that position must be a point in the spherical surface.
KeywordsConfiguration Space Generalize Coordinate Nonholonomic Constraint Virtual Displacement Holonomic Constraint
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