Reaction forces of singular pendulum

Various behavior types of reaction forces and Lagrange multipliers for the case mechanical systems with configuration space singularities are studied in this paper. The motion a one-dimensional double pendulum (or singular pendulum) transversal point or first order tangency is considered. Properties depends on constraint line which free vertex moves along. Configuration could be represented by two smooth curves torus without common points, transversely intersecting first-order tangency. In to study motion, two-dimensional found. expressions obtained analytically angular coordinates. transverse intersection it proved that must zero at point. singularity, nonzero multiplier along ellipse becomes unlimited near Two mechanisms different type points described: nonsmooth broken pendulum. There no regular passing through spaces these systems. pendulum, undefined when passed. makes jump from finite value an infinite one.