Hamilton's Principle

Physical Law

In a conservative field, the motion of a mechanical system can be characterized by requiring that:

$\ds \int_{t_1}^{t_2} \paren {T - V} \rd t$

where:

$T$ denotes the kinetic energy

$V$ denotes the potential energy

be stationary in an actual motion during the time interval from $t_1$ to $t_2$.

Proof

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Also see

• Definition:Calculus of Variations

Source of Name

This entry was named for William Rowan Hamilton.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hamilton's principle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hamilton's principle