All Questions
Tagged with classical-mechanics vector-fields
41
questions
2
votes
1
answer
87
views
How to compute the vector field from a potential in the complex plane?
I am watching this Youtube video and I have the following dumb question around 1:18:00: How do you draw the vector field for a given potential in the complex plane? He gives the potential $V(x) = x^4-...
- 123
1
vote
3
answers
102
views
The conservative force [closed]
I read about the definition of the curl.
It's the measure of the rotation of the vector field around a specific point
I understand this, but I would like to know what does the "curl of the ...
- 11
0
votes
0
answers
64
views
Hamiltonian flows and Poisson Brackets confusion
I have been using results from this paper in calculations. In sections 2.4 and 3.4 they perform a canonical transformation into new coordinates consisting of constants of motion.
My question is ...
- 298
9
votes
4
answers
2k
views
Time evolution operator in classical mechanics?
Hamilton's equation can be written in terms of Poisson brackets, as follows:
$$\dot{q} = \{q,H\}$$
$$\dot{p} = \{p,H\}$$
where $H$ is the Hamiltonian of the system. Now, wikipedia says that the ...
- 1,123
-3
votes
3
answers
309
views
Why is vector calculus so much more important in classical electrodynamics than in classical mechanics?
In this question "vector calculus" refers to the integration and differentiation of vector fields.
Why is vector calculus so much more important in classical electrodynamics than in ...
- 111
0
votes
1
answer
174
views
Curl of a velocity [closed]
In classical mechanics, is the curl of $\vec{v}$ always zero? As $\nabla$ is in position space and not in velocity space ($\nabla_v$). What am I missing regarding $\nabla$ operator in different spaces?...
user292464
2
votes
1
answer
199
views
What is the vector field associated with potential energy?
The mere concept of a line integral is defined for a vector field, and I thus thought the following was a rigorous and general definition of potential energy:
Definition: Given a conservative force ...
- 379
0
votes
1
answer
26
views
Calculating work done when the lower bound of integral is greater than the upper bound
In this video, Dr. Peter Dourmashkin explained friction as an example of a force by which the work done is not path independent. In $2$$:$$50$ min of the video, when we're coming back, he said, $d\...
1
vote
2
answers
129
views
Time derivative of unit velocity vector?
Let's say I have some parametric curve describing the evolution of a particle $\mathbf{r}(t)$. The velocity is $\mathbf{v}(t) = d\mathbf{r}/dt$ of course. I am trying to understand what the expression ...
-1
votes
1
answer
37
views
Conservation and potential with non-cartesian forces
I understand how to determine if a force is conservative from
\begin{equation}
\nabla\times \mathbf{F}=0 \implies \mathbf{F}\text{ is conservative}
\end{equation}
When $F$ is in cartesian coordinates.
...
- 19
3
votes
0
answers
85
views
About the equation $\frac {d^2} {dt^2}\vec x(t) = \nabla \times \vec F(x(t))$. Motion in a curl vector field
I was wondering if there is a physical interpretation of ODEs of the form
$$\frac d{dt}\vec x(t)=\vec y(t)$$
$$ \frac d{dt} \vec y(t) = \nabla \times \vec F(x(t))$$
(or equivalently $\frac {d^2} {dt^2}...
- 208
3
votes
2
answers
154
views
Vector function of vectors expansion
I am reading Landau's Mechanics. In the solution to the problem 4 on page 138, section 42, it is stated that an arbitrary vector function $\vec f(\vec r,\vec p)$ may be written as $\vec f=\vec r\phi_1+...
- 611
0
votes
1
answer
203
views
Displacement vector for rotational motion
When I try to find out how to compute work for rotational motion. I found an equation from a book online with a figure and equation as follows:
$ \vec{s}\ =\vec{\theta}\ \times\vec{r} $
$Thus,$
$d\...
- 135
3
votes
1
answer
82
views
Do all Joukowski aerofoils violate no-penetration condition at trailing edge?
In our fluids course we calculated the velocity distribution around a completely symmetric Joukowski aerofoil (as shown below) and used the Kutta condition to ensure that the velocity was not infinite ...
- 2,604
1
vote
1
answer
66
views
Conditions on $\phi$ and $\boldsymbol{A}$ for when $\boldsymbol{B}$ is uniform
I'm reading "Classical Mechanics" (5ed) by Berkshire and Kibble, in the example for uniform magnetic field on pg.243 (Chapter 10 Lagrangian Mechanics) I came across this
A charged particle ...
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