XV. On a general method in dynamics; by which the study of the motions of all free systems of attracting or repelling points is reduced to the search and differentiation of one central relation, or characteristic function

@article{HamiltonXVOA,
  title={XV. On a general method in dynamics; by which the study of the motions of all free systems of attracting or repelling points is reduced to the search and differentiation of one central relation, or characteristic function},
  author={William Rowan Sir Hamilton},
  journal={Philosophical Transactions of the Royal Society of London},
  pages={247 - 308}
}
  • W. Hamilton
  • Mathematics
  • Philosophical Transactions of the Royal Society of London
The theoretical development of the laws of motion of bodies is a problem of such interest and importance, that it has engaged the attention of all the most eminent mathematicians, since the invention of dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton. Among the successors of those illustrious men, Lagrange has perhaps done more than any other analyst, to give extent and harmony to such deductive researches, by… 

Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations: A Study in the Interaction of Mathematics and Physics

TLDR
Some aspects of the interaction of mathematical analysis and theoretical mechanics during the period 1700–1900 are discussed, with attention to the relatively classical example of the calculus of variations on the one hand, and Hamilton-Jacobi theory on the other.

Reply by Author to C. D. Bailey

Dr. Simkin's example 2, the linear oscillator, was demonstrated in Ref. 2 without the necessity of Lagrange multipliers and equations of constraint. The direct analytical solution to a nonlinear

Interactions between mechanics and differential geometry in the 19th century

Conclusion79. This study of the interaction between mechanics and differential geometry does not pretend to be exhaustive. In particular, there is probably more to be said about the mathematical side

Reply by Author to C.V. Smith Jr. and D.R. Smith

of the approximate solution if one blindly extended the integrations to r = 28 sec using the same values of tI and TV as used for smaller values of tl We believe that Ref. 4, when properly

Lambert’s Theorem: Geometry or Dynamics?

  • A. Albouy
  • Mathematics
    Celestial Mechanics and Dynamical Astronomy
  • 2019
Lambert's theorem (1761) on the elapsed time along a Keplerian arc drew the attention of several prestigious mathematicians. In particular, they tried to give simple and transparent proofs of it (see

The Principle of Least Action as Interpreted by Nature and by the Observer

In this paper, we show that the difficulties of interpretation of the principle of least action concerning "final causes" or "efficient causes" are due to the existence of two different actions, the

A modification of the special theory of relativity

Light, when constructed in terms of the elementary quanta of light, may be viewed in particle‐like or wave‐like terms. The elementary quanta of light, when placed in motion through space/time at a
...