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 q1 and
q2, provided that by the equation of the given surface in rectangular coordinates and
the equations formed by writing q1 and q2 equal to their values in terms of x,y, and z
the last-named coordinates may be uniquely obtained as explicit functions of q1 and
q2.
If the particle is constrained to move in a given path, any specified function of x,y,z may be taken
as its coordinate q1, provided that by the two rectangular equations of its path and the equation
formed by writing q1 equal to its value in terms of x,y,z the last-named coordinates may be
uniquely obtained as explicit functions of q1.
