A vectorial form for the conic variational equations

Hestenes, David

doi:10.2514/3.19784

Cited by 3 publications

(1 citation statement)

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“…Edelbaum's report 51 in 1969 uses this model. Lancaster, 52 Berreen and Sved, 53 Hestenes, 54 and recently Garrison et al 55 used linearization with respect to orbital elements to examine relative motion of particles in elliptic orbits. References to work by Marec and others can be found in Marec's book.…”

Section: Parametric Linearizationmentioning

confidence: 99%

State Transition Matrices for Terminal Rendezvous Studies: Brief Survey and New Example

Carter

1998

Journal of Guidance, Control, and Dynamics

266

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A brief survey and classi cation of much of the published material on linearized rendezvous is presented. This is followed by a new form of solution of the terminal rendezvous problem that is valid in a general central force eld. This solution and the solution of the related adjoint system are used to construct a general state transition matrix. Because of the generality of the assumptions, this state transition matrix is very concise and exible. Finally, the work is applied to the problem of terminal rendezvous near any Keplerian orbit in a Newtonian gravitational eld using the Tschauner-Hempel equations. Because this solution is presented in terms of the true anomaly, considerable care is taken to avoid the types of singularities that are typical in this kind of problem. The result is a state-transition matrix for linearized rendezvous studies that is thought to be simpler and more convenient than other versions found in the literature.

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