Abstract
Stability conditions and equilibrium points of the Kovalevskaya's top are decided by equilibrium point analysis of the non-dimensional Euler's equation. Two parameters which regulate an amount of disturbance of initial value are introduced into the angular velocities of the equilibrium points, because two harmonic oscillations exist near them. Then, non-dimensional Hamilton's canonical equations which are not separable, and their initial conditions are derived. The symplectic method is adopted for numerical integration followed by a compensation process. It modifies the values of the canonical variables so as to cancel the errors of the Hamiltonian only. Error of the Kovalevskaya integral is automatically controlled.
