VII. Second essay on a general method in dynamics

@article{HamiltonVIISE,
  title={VII. Second essay on a general method in dynamics},
  author={William Rowan Sir Hamilton},
  journal={Philosophical Transactions of the Royal Society of London},
  pages={144 - 95}
}
  • W. Hamilton
  • Mathematics
  • Philosophical Transactions of the Royal Society of London
The former Essay contained a general method for reducing all the most important problems of dynamics to the study of one characteristic function, one central or radical relation. It was remarked at the close of that Essay, that many eliminations required by this method in its first conception, might be avoided by a general transformation, introducing the time explicitly into a part S of the whole characteristic function V; and it is now proposed to fix the attention chiefly on this part S, and… 

Hamilton Principle in Piola’s work published in 1825

In this paper we assess how a version of Hamilton Principle is formulated by Piola in his Memoir composed between 1822 and 1824 and published in 1825. The Italian title being Sull’applicazione de’

Identification of localized structure in a nonlinear damped harmonic oscillator using Hamilton's principle

In the mid-seventeenth century Isaac Newton formalized the language necessary to describe the evolution of physical systems. Newton argued that the evolution of the state of a process can be

Mixed convolved action principles in linear continuum dynamics

The paper begins with an overview of several of the classical integral formulations of elastodynamics, which highlights the natural appearance of temporal convolutions in the reciprocal theorem for

Natural selection for least action

The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary

An Overview and Recent Advances in Vector and Scalar Formalisms: Space/Time Discretizations in Computational Dynamics—A Unified Approach

TLDR
An overview of recent advances in computational dynamics for modeling and simulation is described, with particular focus towards general numerical discretizations in space and/or time for N-body and continuum-elastodynamics applications which are encountered in a wide class of holonomic-scleronomic problems.

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

Hamilton's Principle, Hamilton's Law—6" Correct Formulations

The standard formulation of Hamilton's principle requires the knowledge of the initial and end coordinates of a given dynamic system. Any attempt to use this principle for direct calculations without

On the lower-order theories of continua with application to incremental motions, stability and vibrations of rods

The relative merit of lower-order theories, which have been deduced from the three-dimensional theories of continua, is evaluated with respect to the quantified and un-quantified errors in
...