D'alembert's Principle
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 time
derivative
of the
generalized momenta
of the system itself along an
infinitesimal
displacement
compatible with the
constraints
of the system, is zero. That is:
\sum_{i}\left({ {\mathbf F}_{i} - \dot {\mathbf p}_{i} }\right) \cdot \delta{\mathbf r}_{i} = 0.
The principle is also known as the
principle of virtual work
.
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