Physical approach to the theory of constrained motion

A mathematically elementary approach based entirely on Newton’s laws of motion and physical arguments to the problem of constrained motion subjected to general velocity-dependent constraints is presented. Natures of constraint forces are extracted from constraint relations and, consequently, the equations of motion in Newton’s, Lagrange’s, and Appell’s form are obtained. D’Alembert’s principle is proved to be true for and only for holonomic constraints and constraints homogeneous in velocity dependence.