On the Numerical Integration of Lagrange's Top Keeping the First Integral Value Fixed

Abstract

  Numerical integration of Lagrange's top is generally not executed without deviation of the first integral value. In this paper, a new method that the deviation of Hamiltonian is fed back negatively to state variables θ, ρ_θ is proposed. Each feedback quantity is proportional to the corresponding partial derivative of the first integral. Simulation results show that the integration deviation of the first integral keeps zero neighborhood by the method.