Motion of the heavy symmetric top when magnitudes of conserved angular momenta are different: https://arxiv.org/abs/2011.09348
A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the beginning, but the top's overall precession can be positive; or initially, the gyroscope spins in one direction, but in a later stage one can find it while spinning in the other direction. On the other hand, if one knows different properties and types of motion, one can know what will happen. In this work, we have studied the classification of motion type by using constants of motion and showed some mistakes in previous works including Routh's one. We have also studied changes in dynamic variables. We have given examples of different types of motion and solved them numerically.