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The diierent types of energy surfaces are identiied for the Kovalevskaya problem of rigid body dynamics, on the basis of a bifurcation analysis of Poincar e surfaces of section. The organization of their foliation by invariant tori is qualitatively described in terms of Poincar e-Fomenko stacks. The individual tori are then analysed for sets of independent… (More)

- H R Dullin, P H Richter, A P Veselov
- 1998

An explicit formula for the action variables of the Kovalevskaya top as certain abelian integrals of third kind on the Kovalevskaya curve is found. The linear system of diierential equations of Picard-Fuchs type describing the dependence of these variables on the integrals of the Kovalevskaya system is presented in the explicit form. The results are based… (More)

The phenomenon of the wandering point on a blank sheet of paper in serial reproductions is the starting point of an investigation of the perceptual field structure of homogeneous stimulus areas; 609 stimulus points distributed regularly in 21 rows and 29 columns on a DIN A4 sheet were presented successively to 10 subjects and had to be reproduced… (More)

Energy surfaces in the space of action variables are calculated and graphically presented for general triaxial ellipsoidal billiards. As was demonstrated by Jacobi in 1838, the system may be integrated in terms of hyperelliptic functions. The actual computation, however, has never been done. It is found that generic energy surfaces consist of seven pieces,… (More)

- Holger R Dullin, Peter H Richter, Alexander P Veselov, Holger Waalkens
- 2000

The Neumann system describing the motion of a particle on an n-dimensional sphere with an anisotropic harmonic potential, has been celebrated as one of the best understood integrable systems of classical mechanics. The present paper adds a detailed discussion and the determination of its action integrals, using differential equations rather than standard… (More)

The classical and quantum mechanics of a spherical pendulum are worked out, including the dynamics of a suspending frame with moment of inertia . The presence of two separatrices in the bifurcation diagram of the energy-momentum mapping has its mathematical expression in the hyperel-liptic nature of the problem. Nevertheless, numerical computation allows to… (More)

- P H Richter
- 2010

OVERVIEW The paper gives the mathematical concept as well as an algorithm that efficiently tackles the optimal path problem considering turn restrictions. The internal graph representation remains unchanged apart from the necessary assignment of turn restriction. The algorithm develops Reverse Optimal Path Graphs (ROPGs) that are not necessarily cycles-free… (More)

A comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed attracting centers is given, first classically and then quantum mechanically in semiclassical approximation. The system was originally studied in the context of celestial mechanics but, starting with Pauli's dissertation, became a model for one-electron molecules such… (More)