Abstract
Whether maximizing or minimizing something, the important point is that the world line of a particle is the solution of a variational problem in which a certain functional of the trajectory is extremized. In physics, it is conventional to call this functional the action.
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Notes
- 1.
The covariant proper time derivative may be used to generalize the concept of Fermi–Walker transport (see Sect. 2.3 in Chap. 2) to arbitrary Riemannian manifolds. A tensor ? is said to be Fermi–Walker transported along a curve having unit tangent vector u ? if it satisfies the equation \(\dot{\phi}=(u^\mu\dot{u}_\nu-\dot{u}^\mu u_\nu)G_{\mu}^\nu\phi.\)
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© 2011 Springer-Verlag Berlin Heidelberg
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DeWitt, B., Christensen, S.M. (2011). The Free Particle: Geodesics. In: Christensen, S. (eds) Bryce DeWitt's Lectures on Gravitation. Lecture Notes in Physics, vol 826. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36911-0_5
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DOI: https://doi.org/10.1007/978-3-540-36911-0_5
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