Mathematics
Scientific paper
Jun 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986mecc...21...71m&link_type=abstract
Meccanica (ISSN 0025-6455), vol. 21, June 1986, p. 71-74. CNR-sponsored research.
Mathematics
6
Artificial Satellites, Degrees Of Freedom, Euler-Lagrange Equation, Orbital Mechanics, Spacecraft Trajectories, Angular Momentum, Matrices (Mathematics), Partial Differential Equations
Scientific paper
A family of curves in the n-dimensional configuration space (Sn) of a holonomic system with n degrees of freedom is considered. First-order partial differential equations are obtained for the potential function (U) of forces under which any trajectory belonging to the given family of curves can be described by the representative point of the system. The potential function U is written on the assumption that, in addition to the energy integral, a first integral of motion linear in the Lagrangian velocities is assigned. Next the compatibility conditions between the energy constant E, the parameter alpha which appears in the first integral, and the n-1 geometric constants which characterize the family of trajectories are obtained. Finally, two simple examples are discussed.
Borghero Francesco
Melis Andrea
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