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generalized coordinates for constrained motion (Topic)

If the particle is constrained to move on some given surface, any two independent specified functions of its rectangular coordinates $x, y, z$, may be taken as its coordinates $q_1$ and $q_2$, provided that by the equation of the given surface in rectangular coordinates and the equations formed by writing $q_1$ and $q_2$ equal to their values in terms of $x, y$, and $z$ the last-named coordinates may be uniquely obtained as explicit functions of $q_{1}$ and $q_2$.

If the particle is constrained to move in a given path, any specified function of $x,y,z$ may be taken as its coordinate $q_1$, provided that by the two rectangular equations of its path and the equation formed by writing $q_1$ equal to its value in terms of $x,y,z$ the last-named coordinates may be uniquely obtained as explicit functions of $q_1$.



"generalized coordinates for constrained motion" is owned by bloftin.

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See Also: generalized coordinates for free motion


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example of generalized coordinates for constrained motion on a horizontal circle (Example) by bloftin

Cross-references: functions

This is version 1 of generalized coordinates for constrained motion, born on 2008-07-21.
Object id is 290, canonical name is GeneralizedCoordinatesForConstrainedMotion.
Accessed 545 times total.

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Physics Classification: 45.20.Jj (Lagrangian and Hamiltonian mechanics)
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