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Astron. Astrophys. 343, 325-332 (1999)

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2. Stationary and axisymmetric field

In Euclidean space and in ellipsoidal coordinates [FORMULA], related to the Cartesian coordinates [FORMULA] by

[EQUATION]

the kinetic energy of a particle of mass m is

[EQUATION]

where a is a non-negative constant of the dimension of length and the dot denotes differentiation with respect to the time parameter [FORMULA] (normalized so that the momentum is [FORMULA]). The motion of the particle in a stationary axisymmetric potential [FORMULA] is described by equations

[EQUATION]

where we denote, for example,

[EQUATION]

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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