Answer by NinjaDarth for How do I show that there exists variational/action...
Suppose you have a system whose kinematics are given by a list of $N$"configuration" variables $q = \left(q^a: 0 ≤ a < N\right)$, for some number $N = 1, 2, 3, ⋯$ of "degrees of freedom" of the...
View ArticleAnswer by Bence Racskó for How do I show that there exists variational/action...
Remark: I have decided to rework this answer completely. I was unhappy with it and it was incomplete. I have replaced functional derivatives as the main tool with Euler and Helmholtz operators as it is...
View ArticleAnswer by joseph f. johnson for How do I show that there exists...
Obviously one can mathematically cook up equations of motion that would not arise from an action principle. The original motivation for believing that Nature obeys a Law of Least Action was...
View ArticleAnswer by Qmechanic for How do I show that there exists variational/action...
I) Not all equations of motion (eom) are variational. A famous example is the self-dual five-form in type IIB superstring theory. In classical point mechanics, frictional forces typically lead to...
View ArticleHow do I show that there exists variational/action principle for a given...
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's...
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