Variational principles of second, first and intermediate kinds for non-holonomic mechanics

Abstract

The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral variational principles of second kind are set up. From the latter, the general relation of δq′-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only all previous relations of δq′-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds are pointed out.