All Questions
Tagged with classical-mechanics vector-fields
41
questions
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What is the curl of $k\hat{r}/r^n$?
I'm trying to find the curl of ${\bf F}(r) = k \hat{r}/r^n$. I think that this converts to:
$$
k\left(\frac{\hat{x}}{r} + \frac{\hat{y}}{r} + \frac{\hat{z}}{r}\right)\frac{1}{(x^2 + y^2 + z^2)^{n/2}}
...
- 13
2
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0
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568
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Torque of a distributed load: Integrating with dF vs using resultant force
We have a rod that rotates around an fixed point A, which coincides with the end of the rod. The mass distribution along the rod is uniform. We know that the torque generated by the force field at ...
- 556
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215
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Solenoidal forces
As far as I know a solenoidal vector field is such one that
$$\vec\nabla\cdot \vec F=0.$$
However I saw a book on mechanics defining a solenoidal force as one for which the infinitesimal work ...
- 17.8k
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Clarification about some steps in the derivation of the Lie derivative (mechanics)
First of all, this question may seem to be undefined, because I'm not sure how to connect this (to me) newly introduced concept with the abstract notion of the Lie derivative. I'm not even sure if I ...
- 912
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2
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105
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What is the meaning of this definition of potential energy?
The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
6
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1
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Hamiltonian flow?
I was wondering what the Hamiltonian flow actually is?
Here is my idea, I just wanted to know if I am correct about this.
So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and $...
- 97
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2
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What are the mathematical models for force, acceleration and velocity?
In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
- 905
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Lagrangian vector field expression
The Lagrangian vector field $X_L$ on the tangent bundle is given in page 4 of Marco Mazzucchelli's "critical Point Theory for Lagrangian systems" to be;
\begin{equation}
X_L=\sum^M_{j=1}\bigg(v^j\frac{...
- 2,441
11
votes
2
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1k
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Does Hamilton Mechanics give a general phase-space conserving flux?
Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltonian theory like the flux of an ideal fluid, which doesn't change ...
- 175
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In a gas of particles, how is the displacement vector related to the number density?
Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector ...
- 852
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Simulation of physics of chains/ropes in force fields resources?
I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting ...
- 297