Lie transformation
1.The main purpose of this dissertation is to study the problems of symmetries and conserved quantities of controllable nonholonomic systems and mechanico-electrical dynamical systems, based on the invariance of the Hamilton action under the infinitesimal Lie group transformation.
2.We apply Lie group method and Cayley transformation to construct high order explicit square conserving scheme for the modulus conserving differential equations, such as the Euler equation, the Landau-Lifshitz equation and compare the numerical results with the classical Runge-Kutta method in modulus conserving and accuracy. Numerical experiments results show that the new explicit square conserving scheme can preserve the modulus conserving property and the same accuracy as the corresponding classical Runge-Kutta methods.
3.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?
