Hamilton's equations of motion
Safko, John L. Formerly, Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina.
Stehle, Philip Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania.
- Phase space
- Additional Reading
A set of first-order ordinary differential equations that may be used to describe the motion of a mechanical system. Because of their remarkably symmetrical form [which appears in Eqs. (4), below], they are often referred to as the canonical equation of motion (where “canonical” is used in the sense of designating a simple general set of standard equations). The Lagrangian formulation of a system of f degrees of freedom generates f differential equations of second order in the time derivatives of the variables. Hamilton's equations, which are equivalent to Lagrange's equations, consist of 2f first-order and highly symmetrical equations. These properties make Hamilton's equations very useful for general discussions of the motion of systems. See also: Degree of freedom (mechanics); Differential equation; Lagrange's equations
The content above is only an excerpt.
for your institution. Subscribe
To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.
to your librarian. Recommend
Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.
AccessScience provides the most accurate and trustworthy scientific information available.
Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Contributors include more than 9000 highly qualified scientists and 43 Nobel Prize winners.
MORE THAN 8700 articles covering all major scientific disciplines and encompassing the McGraw-Hill Encyclopedia of Science & Technology and McGraw-Hill Yearbook of Science & Technology
115,000-PLUS definitions from the McGraw-Hill Dictionary of Scientific and Technical Terms
3000 biographies of notable scientific figures
MORE THAN 19,000 downloadable images and animations illustrating key topics
ENGAGING VIDEOS highlighting the life and work of award-winning scientists
SUGGESTIONS FOR FURTHER STUDY and additional readings to guide students to deeper understanding and research
LINKS TO CITABLE LITERATURE help students expand their knowledge using primary sources of information