Geodesic
Particle trajectories on manifolds – some remarks on harmonic oscillator on a sphere
Mathematica Applicanda, Tome 47 (2019) no. 1, pp. 45-59.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The classical harmonic oscillator with spherical configuration space is studied. The equations of motion are derived from Hamiltonian formulation of mechanics and approximate solutions in some special cases are obtained. A reliable symplectic integrator is used to obtain numerical solutions which are then compared with analytical approximations. The overall impact of positive curvature on the solutions is discussed and illustrated with comparison of solutions on cylindrical and spherical surfaces.
DOI : 10.14708/ma.v47i1.6362
Classification : 34C15;34B60;70H05
Mots-clés : harmonic oscillations;configuration manifolds;approximate solutions;symplectic integrators 
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Kacper Stefan Chyła. Particle trajectories on manifolds – some remarks on harmonic oscillator on a sphere. Mathematica Applicanda, Tome 47 (2019) no. 1, pp.  45-59. doi : 10.14708/ma.v47i1.6362. http://geodesic.mathdoc.fr/articles/10.14708/ma.v47i1.6362/

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