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