Titlebook: Global Aspects of Classical Integrable Systems; Richard H. Cushman,Larry M. Bates Book 2015Latest edition Springer Basel 2015 algebra.clas

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The Lagrange topPhysically, the Lagrange top is a symmetric rigid body spinning about its figure axis whose base point is fixed. A constant vertical gravitational force acts on the center of mass of the top, which lies on its symmetry axis.

Tartar

Systems with SymmetryIn this chapter we discuss Hamiltonian systems with symmetry. By a symmetry of a Hamiltonian system (H, ., .) we mean a proper action of a Lie group G on a symplectic manifold (., .), which has a momentum mapping .: . → g*, and preserves the Hamiltonian ..

fleeting

Action-angle coordinatesHere we prove the existence of local action angle coordinates for a Liouville integrable Hamiltonian system near a compact connected fiber of its integral mapping.

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Richard H. Cushman,Larry M. BatesThis book gives a complete global geometric description of the motion of the two dimensional harmonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top.This bo

Throttle

hangdog

Geodesics on ,,verns the motion of two bodies in .. under gravitational attraction. We give two methods to regularize the flow of the Kepler vector field: one energy surface by energy surface and the other for all negative energies at once.

CHASE

acquisition

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Basic Morse Theoryh manifold and show that if it is nondegenerate then there are local coordinates in which the function is equal to its second derivative. We also prove the Morse isotopy lemma which gives a criterion when two suitable level sets of a smooth function are diffeomorphic. We conclude the chapter by exte