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-1 votes

Relation between energy and time

I understand the question as the OP asking of an intuitive way to think about the relation between energy and time. Therefore the point I would like to make is that energy isn't really a thing. So for ...
Javatasse's user avatar
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2 votes

Relation between energy and time

The way I like to look at it (and which may or may not give you the same amount of intuition as it does to me) is as such: Momentum is what gives rise to changes in position. Clasically, a body ...
CompassBearer's user avatar
5 votes

Relation between energy and time

Why is energy always related to time in physics. I don't think it is helpful to describe energy as "always related to time" in physics. That being said, there certainly are a number of ...
hft's user avatar
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1 vote

Validity of $\mbox{d}H/\mbox{d}t=\partial H/\partial t$ for dissipative systems

I'll split my answer in some paragraphs: 1. Newton's mechanics in strong and weak forms; 2. Lagrangian mechanics; 3. Hamiltonian mechanics. 1.a Newton's mechanics: strong form. Newton's second ...
basics's user avatar
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15 votes
Accepted

Relation between energy and time

There are at least three occasions where the notions of Energy and Time show up together in classical and modern physics. Probably the most elementary situation is related to the fact that the ...
Valter Moretti's user avatar
5 votes

Validity of $\mbox{d}H/\mbox{d}t=\partial H/\partial t$ for dissipative systems

In principle you can use Hamiltonian mechanics also for dissipative systems, or fon systems which cannot be completely described by a Lagrangian. When a Lagrangian is provided, the Legendre ...
Valter Moretti's user avatar
6 votes
Accepted

Is it possible to understand in simple terms what a Symplectic Structure is?

At the most rough level possible, a symplectic structure (geometrically) is an even-dimensional manifold together with a preferred choice of two-dimensional planes which, taken together, span the ...
11zaq's user avatar
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2 votes
Accepted

Meaning of $d\mathcal{L}=-H$ in analytical mechanics?

I think it is gibberish in your own words. $\frac{\partial}{\partial \dot{q}}$ cannot be replaced by $dt \frac{\partial}{\partial {q}}$ even in the most cavalier approach because $\dot{q} = \frac{dq}{...
John's user avatar
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1 vote

Meaning of $d\mathcal{L}=-H$ in analytical mechanics?

Apart from the fact that I am really skeptical about its mathematical validity, your replacement $\frac{\partial}{\partial\dot{q}}\rightarrow\frac{dt}{\partial q}$ makes little sense in the context of ...
paulina's user avatar
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0 votes

Volume preserving transformation in the Circular Restricted Three-Body problem

OP is right that OP's map (1) $$(x,y,p_x,p_y)\quad\stackrel{f}{\mapsto}\quad (x,y,v_x,v_y)$$ is volume preserving $$ f^{\ast}(\omega\wedge\omega)~=~ \omega\wedge\omega, $$ although not a ...
Qmechanic's user avatar
  • 206k
0 votes

Is it possible there can be a non-Fourier model of string vibration? Is there an exact solution?

Assuming linearity, the response of the system can be written as the superposition of its modes. How many modes does a continuous medium have? An infinite number, in general. How many modes have non-...
basics's user avatar
  • 10.7k
2 votes

Is it possible there can be a non-Fourier model of string vibration? Is there an exact solution?

A vibrating string can support a very large number of vibrational modes simultaneously. This is because waves on strings superimpose linearly. Note here that an electric guitar string struck hard with ...
niels nielsen's user avatar
0 votes

Equivalence between Hamiltonian and Lagrangian Mechanics

Lagrangian and Hamiltonian mechanics are not exactly equivalent because they do not cover the same possibilities for the system to be described. Actually, just using the Newtonian laws gives yet ...
Jos Bergervoet's user avatar
2 votes
Accepted

What is the determinant of the Wheeler-DeWitt metric tensor constructed from spatial metrics in ADM formalism?

The Wheeler-DeWitt metric $$\begin{align} G~=~&G_{IJ}(\mathrm{d}y\odot\mathrm{d}y)^I\odot(\mathrm{d}y\odot\mathrm{d}y)^J\cr ~=~&G_{i_1i_2,j_1j_2}(\mathrm{d}y^{i_1}\odot\mathrm{d}y^{i_2})\odot(\...
Qmechanic's user avatar
  • 206k
0 votes
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Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates

There are some issues in your computation. It seems that you assume that you will be able to use identities from the 1D harmonic oscillator to solve for AA coordinates in this more general case. This ...
Void's user avatar
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2 votes

What does the optical Hamiltonian mean?

OP's square root Hamiltonian taken from Ref. 1 can more systematically be derived as follows: We start by identifying the optical length with a square root action$^1$ $$\begin{align}S_0[{\bf r}]~=~&...
Qmechanic's user avatar
  • 206k
2 votes

What does the optical Hamiltonian mean?

You can view it as $H = p_3$, the momentum component in the third direction. It is analogous to relativity where you view energy as the time comment of 4-momentum. Similarly, the components are not ...
LPZ's user avatar
  • 13.1k
2 votes

Hamiltonian formalism of General Relativity Textbook

Here are some additional references: General Relativity: A Concise Introduction by Steven Carlip Chapter 12 of this book has a concise and accessible introduction to the Hamiltonian formalism. ...
1 vote

Is it possible to derive Schrödinger's equation from Hamilton's equations?

First of all, it should be stressed that the TDSE (1) cannot be derived from classical physics alone, cf. e.g. this Phys.SE post. However, assuming that the classical system at hand can be quantized, ...
Qmechanic's user avatar
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