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

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. Project supported by the National Natural Science Foundation of China (Grant No. 19272064).