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euler-lagrange_equations [2015/03/29 18:52] nikolaj |
euler-lagrange_equations [2015/03/29 18:57] nikolaj |
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| | @#BBDDEE: let | @#BBDDEE: $\diamond\ q(t)$ | | | @#BBDDEE: let | @#BBDDEE: $\diamond\ q(t)$ | | ||
| | @#BBDDEE: let | @#BBDDEE: $\diamond\ L(x^1,\dots,x^s,v^1,\dots,v^s,t)$ | | | @#BBDDEE: let | @#BBDDEE: $\diamond\ L(x^1,\dots,x^s,v^1,\dots,v^s,t)$ | | ||
| - | | @#DDDDDD: range | @#DDDDDD: $j\in\mathrm{range}(s)$ | | + | | @#DDDDDD: range | @#DDDDDD: $j\in\{1,\dots,s\}$ | |
| | @#55EE55: postulate | @#55EE55: $\left(\dfrac{\mathrm d}{\mathrm dt}\dfrac{\partial L}{\partial v^j}\right)(q,q',t) - \dfrac{\partial L}{\partial x^j}(q,q',t) = 0$ | | | @#55EE55: postulate | @#55EE55: $\left(\dfrac{\mathrm d}{\mathrm dt}\dfrac{\partial L}{\partial v^j}\right)(q,q',t) - \dfrac{\partial L}{\partial x^j}(q,q',t) = 0$ | | ||
