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A Principle in classical mechanics with a ‘relativistic’ path-element extending the principle of least action

Published online by Cambridge University Press:  24 October 2008

Edgar B. Schieldrop
Affiliation:
University of Oslo

Extract

1. A particle with mass m and coordinates x1x2, x3 relative to a set of rectangular axes fixed in Newtonian space is moving in a field of conservative forces with a potential energy V(x1, x2, x3) and a kinetic energy

The equations of motion, written

(representing the three equations i = l, i = 2, i = 3 in a way to be used in this paper), constitute, as they stand, a sufficient condition in order to ensure

in the sense that the Hamiltonian integral has a stationary value if the actual motion is compared with neighbouring motions with the same terminal positions and the same terminal values of the time as in the actual motion.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1955

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