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American Journal of Physics, 1973
It is proven that the modified Hamilton's principle, in which both the coordinates and momenta are varied independently, can be derived from Hamilton's principle in which only the coordinates are varied independently.
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It is proven that the modified Hamilton's principle, in which both the coordinates and momenta are varied independently, can be derived from Hamilton's principle in which only the coordinates are varied independently.
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The Variational Principle of Hamilton
2010It is shown that the linearised equations of motion can also be derived as Euler–Lagrange equations of Hamilton’s variational principle. To this end, a Lagrangian is determined as the difference between the kinetic energy and the sum of the internal and gravitational potential energy of the star.
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Hamilton's principle for beginners
European Journal of Physics, 2007I find that students have difficulty with Hamilton's principle, at least the first time they come into contact with it, and therefore it is worth designing some examples to help students grasp its complex meaning. This paper supplies the simplest example to consolidate the learning of the quoted principle: that of a free particle moving along a line ...
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