All Questions
Tagged with time variational-principle
10
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111
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Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?
This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
- 353
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How to justify drawing out the virtual differential $\delta$ to the front of the integral in the Hamilton principle?
My textbook derives the equivalence of Hamilton principle to d'Alembert's principle as such:
\begin{align}
0&=\int_{t_1}^{t_2}\left(\sum_i(m_i\ddot{\vec{r}}-\vec K_i)\cdot\delta\vec r_i\right)dt=\...
- 95
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Confusion with the variational operator $\delta$ and finding variations
I have recently started studying String Theory and this notion of variations has come up. Suppose that we have a Lagrangian $L$ such that the action of this Lagrangian is just $$S=\int dt L.$$ The ...
- 385
2
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1
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What is the role of time (time interval) in principle of least action?
Action is represented by $S[Q(t)]$ where $Q(t)$ is the name of a single complete path in the configuration space of a system. The path starts at the point $q_i$ and ends at the point $q_f$. Suppose ...
- 1,009
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Smaller elapsed time with higher velocity, but free fall maximize elapsed time, who clearly have a velocity compare to a stationary object
I am a little confused because an object with velocity would experience smaller elapsed time compared to an object that is not. But in GR elapsed (proper) time is maximized by free fall who have ...
0
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1
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34
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Lagrange's equation for system not having time translation
While we are deriving Lagrange's equation from D'Alembert's principle, when we argues as;
$$\delta \vec r_\alpha = \sum_i \frac{\partial \vec r_\alpha}{\partial
q_i }\delta q_i + \frac{ \partial \...
- 2,283
3
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2
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142
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Paths of least action and loops in time
In the book
Quantum Field Theory for the Gifted Amateur
link: https://books.google.ca/books?hl=en&lr=&id=nIk6AwAAQBAJ&oi=fnd&pg=PP1&ots=JZjwG_qDt5&sig=...
- 1,548
6
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How to deal with explicit time dependence of the Lagrangian?
Clearly, if the Lagrangian in explicitly time dependent, the Euler-Lagrange equations being satisfied does not extremise the action. I am unclear as to how to deal with systems with an explicitly time-...
- 3,997
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Timeless description of classical mechanics
The description of J. B. Barbour arXiv:0903.3489, 2009 is considered to be timeless but the term "change" appears in that text.
Essentially, a configuration space is considered: One calculates the ...
3
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How is the physical Lagrangian related to the constrained minimization Lagrangian?
If we're minimizing an energy $V(q)$ subject to constraints $C(q) = 0$, the Lagrangian is
$$L = V(q) + \lambda C(q).$$
I have fairly solid intuition for this Lagrangian, namely that the energy ...
- 213