Analytical Mechanics and its Visualization with Computer Graphics

This review comprises two parts and deals with the Hamiltonian formulation of classical mechanics and relies on the concept of Poisson brackets. In contrast to conventional treatises on the subject, the authors focus on obtaining qualitative information essential for numerical simulation; thus computer graphics are an important instrument for studying mechanical problems. The review includes a range of examples, from the simplest: the spherical pendulum, to the more complex: the soft chaos in the spin dynamics of superfluid helium-3. The systematic use of Poisson brackets allows a natural transition to quantum mechanics. Part II presents a concise description of quantum formalism, mainly within the framework of the Heisenberg approach. Among other physical examples, the authors consider the quantum Kepler problem, and internal symmetries and the related degeneracy of the spectrum. As a conclusion the authors discuss the part played by spatial symmetries in classical and quantum cases, the Einstein, Podolsky and Rosen effect.Golo, V. L. is the author of 'Analytical Mechanics and its Visualization with Computer Graphics', published 2005 under ISBN 9781904868439 and ISBN 1904868436.