Displaying similar documents to “Dynamics of relative motion of test particles in general relativity”

Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.

Ernesto A. Lacomba, J. Guadalupe Reyes (1998)

Publicacions Matemàtiques

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We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves....

Constant Jacobi osculating rank of 𝐔 ( 3 ) / ( 𝐔 ( 1 ) × 𝐔 ( 1 ) × 𝐔 ( 1 ) )

Teresa Arias-Marco (2009)

Archivum Mathematicum

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In this paper we obtain an interesting relation between the covariant derivatives of the Jacobi operator valid for all geodesic on the flag manifold M 6 = U ( 3 ) / ( U ( 1 ) × U ( 1 ) × U ( 1 ) ) . As a consequence, an explicit expression of the Jacobi operator independent of the geodesic can be obtained on such a manifold. Moreover, we show the way to calculate the Jacobi vector fields on this manifold by a new formula valid on every g.o. space.

Constant Jacobi osculating rank of 𝐔 ( 3 ) / ( 𝐔 ( 1 ) × 𝐔 ( 1 ) × 𝐔 ( 1 ) )

Teresa Arias-Marco (2009)

Archivum Mathematicum

Similarity:

In this paper we obtain an interesting relation between the covariant derivatives of the Jacobi operator valid for all geodesic on the flag manifold M 6 = U ( 3 ) / ( U ( 1 ) × U ( 1 ) × U ( 1 ) ) . As a consequence, an explicit expression of the Jacobi operator independent of the geodesic can be obtained on such a manifold. Moreover, we show the way to calculate the Jacobi vector fields on this manifold by a new formula valid on every g.o. space.