All Questions
4
questions
1
vote
0
answers
48
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Find curve minimizing energy loss due to friction [closed]
I am looking for an ansatz of the following problem:
Given a mass $m$ moving in a constant gravitational field along curves $C$ connecting two fixed points I want to find the curve $C_0$ that ...
- 917
0
votes
1
answer
102
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For virtual displacement in the Lagrangian, why is $\delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0$?
I am having trouble understanding why $$\delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0.\tag{7.132}$$
you can see my explanation leading up to it below.
I would greatly ...
- 283
3
votes
3
answers
428
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Lagrangian Derivation of Brachistocrone? [closed]
I've been trying to derive the functional description of the brachistocrone. To do this, I used the Lagrangian to describe motion along a functional path. given a function $ f(x) $ where $0<y<a$ ...
- 610
5
votes
0
answers
101
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Optimal tunnel shape for travelling inside the earth [duplicate]
Say you were to travel from Paris to Tokyo by digging a tunnel between both cities. If the tunnel is straight, one can easily compute that the time for travelling from one city to the other (...
- 993