Ads
related to: hamilton's principle action figure parts and accessories set 1
Search results
Results From The WOW.Com Content Network
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
The action figure is placed on the card and a bubble of clear plastic is then laid over the top of the action figure and attached to the card. The figure is then clearly visible to consumers. Often the bubble will have several small, fitted compartments to hold the figure and its accessories in place.
Action principles are "integral" approaches rather than the "differential" approach of Newtonian mechanics.[2]: 162 The core ideas are based on energy, paths, an energy function called the Lagrangian along paths, and selection of a path according to the "action", a continuous sum or integral of the Lagrangian along the path.
One of the conditions for the applicability of many theorems and equations is that the system must be a holonomic system. For example, if a physical system is a holonomic system and a monogenic system, then Hamilton's principle is the necessary and sufficient condition for the correctness of Lagrange's equation. [3]
Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1] Action and the variational principle are used in Feynman's formulation of quantum mechanics [2] and in general relativity. [3]
Ad
related to: hamilton's principle action figure parts and accessories set 1