The motion for systems subject to constraints is difficult to calculate using Newtonian mechanics because all the unknown constraint forces must be included explicitly with the active forces in order ...The motion for systems subject to constraints is difficult to calculate using Newtonian mechanics because all the unknown constraint forces must be included explicitly with the active forces in order to determine the equations of motion. Lagrangian mechanics avoids these difficulties by allowing selection of independent generalized coordinates that incorporate the correlated motion induced by the constraint forces. This allows the constraint forces acting on the system to be ignored.
\end{equation}\) plane that does not pass through the origin, and we want to find the point on the curve that is its closest approach to the origin. It’s just the ratio of the lengths of the two norma...\end{equation}\) plane that does not pass through the origin, and we want to find the point on the curve that is its closest approach to the origin. It’s just the ratio of the lengths of the two normal vectors (of course, “normal” here means the vectors are perpendicular to the curves, they are not normalized to unit length!) We can find \(\begin{equation}
