| Abstract: | Two new versions of the principle of least constraint are derived from the D'Alembert-Lagrange principle for systems with ideal holonomic and non-holonomic restoring and non-restoring constraints. The first version is similar to Boltzmann's and Bolotov's modification of Gauss's principle for systems with non-restoring constraints. The difference is that here the actual motion is determined in a certain bounded set of possible motions as the one that deviates least from the motion of the system with all non-restoring constraints and any part of the restoring constraints disengaged. According to the second version of the principle, the actual motion is found by comparing certain distinguished possible motions as to their deviation from the motion of the system obtained by eliminating any part of the non-restoring and any part of the restoring constraints. Examples are given. |
