The physical meaning of Gauss’s principle of least constraint is the actual acceleration can be obtained by minimizing the Gaussian function, which is the square of the scaled constraint forces. Thus we can get the solution of equations of motion by solving a minimizing problem without appeal to the use of virtual displacement and the D’Alembert’s principle. This perspective enables Gauss’s principle of least constraint to get the solution of motion for systems having multiple, linear and/or nonlinear, holonomic and/or nonholonomic constraints. In this thesis, we proposed a new form of Gauss’s principle of least constraint, which is based on quasi coordinates of angular velocity, and then applied them to the rotational rigid-body systems with better symmetry. Thus we take the examples of the rigid-body ball and the disk to discuss the behavior of a ball on the surface of a rotating disk and a disk on the plane.