# Tag Info

### How can I interpret the normal modes of this mechanical system?

In this example all the linkage does is convert a displacement of $u_3$ at the top to a displacement of $-\frac ba u_3$ at the bottom instantaneously so you should not expect there to be any ...
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### How can I interpret the normal modes of this mechanical system?

The system you wrote is a system of DAEs (differential-algebraic equations) since the third equation is a algebraic equation representing an algebraic constraints. As the rod is massless, its "...
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### QFT introduction: From point mechanics to the continuum

What do Peskin & Schroeder mean by $\dot{\phi}(\vec{x})$? How can we define a time derivative of a function, which depends on position only? Notation $\dot \phi$, when writing down Lagrangian/...
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### QFT introduction: From point mechanics to the continuum

I know that the four derivative (and the four vector) inside the Lagrangian of (Eq. 2) is crucial to maintain Lorentz invariance, but that is the only thing that is not predicted by the four ...
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### Designing a thought experiment on Noether's Theorem

Experiments on crystals are translationally variant because the crystal structure is only the same up to translations that reproduce the same structure, in such cases there is "crystal momentum&...
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### Non-inertial frames in quantum mechanics

Inertial forces are completely described, in Hamiltonian mechanics, in terms of an electric-like potential plus a magnetic-like vector potential. The Hamiltonian of a free particle in a non-inertial ...
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### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

The notation is a little sloppy from a purely mathematical point of view (although common in physics) so it might be causing a little confusion. To help clarify, it might help to use different letters ...
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### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

They are partial derivatives. From the chain rule, we have $$\frac{\partial V(aq_1-bq_2)}{\partial q_1}= a V'(aq_1-bq_2),\\ \frac{\partial V(aq_1-bq_2)}{\partial q_2}= -b V'(aq_1-bq_2).$$ For ...
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### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

No. The notation means that the V on the RHS is a function only of one variable, and so its derivative is the simplest, one-variable derivative.
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### Invertibility between generalized and actual coordinates

While it is true that you use 3 numbers for Cartesian coordinates, you do not use the full set of triplets. You use the subset that satisfies $x_1^2 +x_2^2 + x_3^2 = r^2$. This subset has two degrees ...
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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 $\dot{q} = \frac{dq}{... • 3,872 1 vote ### Meaning of$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}$makes little sense in the context of ... • 1,811 0 votes ### Why aren't all objects and their images same in size? Dicing with infinities is usually dangerous. Start with the idea that a small part of the object, size o$\times$o, produces an image of size i$\times$i. Now let o become smaller and smaller. What ... • 97.8k 1 vote Accepted ### Work performed by hydrostatic pressure With a little less math, the power of a stress distribution$\mathbf{t}_n$over the boundary of a volume$V$is $$P(t) = \oint_{\partial V} \mathbf{t}_n \cdot \mathbf{u} \ ,$$ being$\mathbf{u}$the ... • 10.5k 0 votes ### Is there an error in Susskinds' derivation of Euler-Lagrange equations? Here are my thoughts (I may be wrong). The first equation states the action which is the integral of the Lagrangian with respect to time. Integrating is the equivalent of finding the areas of strips, ... 2 votes ### Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution? OP asks an interesting question, which we rephrase as follows: Given an action $$S[q]~=~\int_{t_1}^{t_2} \!dt~L(q,\frac{dq}{dt},t),$$ are the stationary action principle (SAP) and Euler-Lagrange (EL) ... • 206k 1 vote Accepted ### How to compute the vector field from a potential in the complex plane? What did you plot exactly, I rather obtained something like this: which is compatible with the lecture. The velocity field is: $$\dot z = w := \sqrt{E-V(z)}$$ with$\min V<E<0$. Since it is ... • 13k 1 vote Accepted ### Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution? As I understand it you are wondering about the following: What will be the implications when Hamilton's action is evaluated over a time interval where the end point is earlier than the start point? I ... • 21.4k 0 votes ### What happens to the coefficient of friction as the normal force increases? Well an old kemps engineers year book I took notes from, gave static coefficient values for cast iron on steel for a number of different pressures, which showed a rise in value with pressure increase. ... 1 vote ### Why the interaction between system and thermal bath does not affect the energy levels of the system? First, let's recall that already in classical theory, Hamiltonian value is not necessarily energy value. Energy is usually defined by some definite expression motivated by a conservation law, which is ... • 39k 0 votes ### Work performed by hydrostatic pressure My intuition is that we are looking at a special case of Stokes' theorem, since we are relating surface integrals to volume changes. To this end, it seems clear enough to me that the differential ... • 722 3 votes ### Would a nearby electron be attracted/repulsed due to the oscillating$\vec E$and$\vec B\$ field of a passing electromagnetic wave?

Suppose $$\vec E (x, t) = \begin{bmatrix}0 \\ E_{max} \cos (kx-\omega t) \\ 0 \end{bmatrix}$$ $$\vec B(x, t) = \begin{bmatrix}0 \\ 0 \\ B_{max} \cos (kx-\omega t) \end{bmatrix}$$ a moving electron ...
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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 ...
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### The conservative force

While @basics has the math right, I understand your question is about the physical interptetation. To answer this, we must understand what a force field is, since the definition of the rotation ...
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