# Tagged Questions

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### Why we do calculus of variation instead of finding maxima or miniama of function? [on hold]

Why we do calculus of variation instead of finding maxima or minima of function? What is the difference between finding maxima or mimima i.e. critical point of a function and calculus of variation?
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### When is numerical value of Lagrangian evaluated on-shell a full differential?

I noticed recently that for many field equations, Lagrangian evaluated on-shell (i.e. using equations of motions) is a full derivative- a divergence or something, or in other words a boundary term. ...
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### Question on basic tensorial calculus on field theory

Working on the Maxwell field as a gauge theory, at some point the following derivative comes up: $\frac{\partial(\partial_iA_0)}{\partial A_0}=0$ which must be, accordingly to the theory, zero. My ...
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### Shape of water on top of a thin sheet of stretched plastic

Consider a thin sheet of plastic (a square sheet for simplicity) that is stretched taught in a plane parallel to the ground. If a volume of water is then placed on top of the thin plastic sheet, then ...
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### What is the path taken by a “cable car”?

A well known result in variational calculus & Lagrangian Mechanics is the solution to the "brachistochrone" problem, where it is found the path connecting two points, A & B such that the time ...
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### Is it possible to derive the shape of the bending plates by use calculus of variations?

Of course the main idea to solve this problem is find the physical quantity which is have smallest or largest value. Iâ€™ve tried some, such as area of surfaces, But I think it canâ€™t be a solution. Does ...
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### How to derive the true spatial paths (orbits) from the Jacobi-Maupertuis condition

How can differential equations describing a physical object's true spatial paths (orbits) be derived from the time-independent Jacobi-Maupertuis principle of least action? According to this, it is ...
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### Calculus of Variations - Virtual displacements

I am currently reading "The Variational Principles of Mechanics - Cornelius Lanczos", in which the author talks about the variation of a function $F(q_1, q_2, \dots q_n)$ where $q_1, q_2, \dots q_n$ ...
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### Classical mechanics principle of least action

I don't understand here what does the book mean by expanding in terms of $\delta{q}$ and $\delta{\dot{q}}$ can someone explain that part.