D'Alembert's principle

From open-encyclopedia.com - the free encyclopedia.

D'Alembert's principle is a statement of the fundamental classical laws of motion. It is equivalent to Newton's second law. It is named after its discoverer, the French physicist Jean le Rond d'Alembert.

The principle states that the sum of the differences between the generalized forces acting on a system and the generalized momenta of the system itself along an infinitesimal displacement compatible with the constraints of the system, is zero. That is:

<math> \sum_{i}\left({ {\mathbf F}_{i} - \dot {\mathbf p}_{i} }\right) \cdot \delta{\mathbf r}_{i} = 0 <math>

The principle is also known as the principle of virtual work.

ja:ダランベールの原理 sl:d'Alembertovo načelo