On the Differential Geometry of Trajectory Deviation with Particular Emphasis on Keplerian Motion

Details On the Differential Geometry of Trajectory Deviation with Particular Emphasis on Keplerian Motion On the Differential Geometry of Trajectory Deviation with Particular Emphasis on Keplerian Motion

Jul 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec...9..483l&link_type=abstract

Celestial Mechanics, Volume 9, Issue 4, pp.483-489

Physics

Scientific paper

The Pontryagin/Lawden scalar product of the deviation phase vector and the adjoint phase vector may be identified with Lagrange's reciprocal formula for two variant motions if the acceleration field is conservative. Hence for two slightly different trajectories with common end-points, the terminal velocity differences must have equal scalar product with Lawden's primer vectors. The final velocity difference is orthogonal to the constant time of flight locus for isoenergetic motions from a common initial point. A Keplerian trajectory behaves like a rigid curve as far as radial deviation is concerned in the case of a small change of direction of the initial velocity vector.

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