Seminar

Geometry, Mechanics and Control Seminar

A geometric approach to Sundman transformation and its applications

Speaker:  José F. Cariñena (Departamento de Física Teórica, Universidad de Zaragoza)
Date:  Friday, 29 October 2021 - 15:30
Place:  Online - us06web.zoom.us/j/7555463367 (ID: 755 546 3367)

Abstract:

A geometric approach to Sundman infitesimal time-reparametrisation is given and some of its applications are used to illustrate the general theory. Special emphasis is put on geodesic motions and systems described by mechanical type Lagrangians. The Jacobi-Maupertuis metric appears as a particular case of a Sundman transformation. The particular case of second-order differential equations will also be analysed.


References

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[2] Levi-Civita, T.: Sur la résolution qualitative du problème restreint des trois corps, Acta Math. 30, 305{327 (1906).

[3] Sundman, K.F.: Mémoire sur le problème des trois corps, Acta Mathematica 36, 105{179 (1913).

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[5] Kavle, H., Offin, D., and Portaluri, A.: Keplerian orbits through theConley-Zehnder index, Qual. Theory Dyn. Syst. 20, 10 (2021).

[6] Cariñena, J.F., Martínez, E., and Muñoz-Lecanda, M.C.: Infinitesimal time reparametrisation and its applications, J. Nonl. Math. Phys.,
submitted (2021).

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[9] Cariñena, J.F., Martínez, E., and Muñoz-Lecanda, M.C.: Sundman transformation and alternative tangent bundle structure, to be submitted(2021).