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Classical Mechanics: Difference between revisions
added Gaudi's hanging strings
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Supposing <math> q_i(t) </math> solves the EL equations for s degrees of freedom, we can analyze properties of the integral across finite time <math> S = \int_{t_1}^{t_2} L(q_1(t), \cdots, q_s(t), \dot{q}_1(t), \cdots, \dot{q}_s(t), t) dt </math>, since substituting the trajectory gives a strict function of time. | Supposing <math> q_i(t) </math> solves the EL equations for s degrees of freedom, we can analyze properties of the integral across finite time <math> S = \int_{t_1}^{t_2} L(q_1(t), \cdots, q_s(t), \dot{q}_1(t), \cdots, \dot{q}_s(t), t) dt </math>, since substituting the trajectory gives a strict function of time. | ||
[[File:Gaudi hanging strings.jpg|thumb|right|Hanging strings and weights used by Gaudi to model the shape of La Sagrada Familia. [http://dataphys.org/list/gaudis-hanging-chain-models/ source]]] | |||
=== Infinite Dimensional Techniques === | === Infinite Dimensional Techniques === | ||