All Questions
13 questions
7
votes
2
answers
1k
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A confusion about notation in Goldstein
On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation
$$\dfrac{d}{dt}{\bf p}_i = {\bf F}_i^{(e)...
- 37.4k
2
votes
1
answer
1k
views
What does a Umlaut (double dot) above an angle mean?
I'm reading a paper on double pendulums and there is an equation of motion that contains a double dot (Umlaut) above an angle. What does this mean / is this a standard notation in equations of motion?...
- 287
2
votes
2
answers
1k
views
Confusing Total Derivative and Partial Derivative in Classical Field Theory - Noether Theorem
I'm really confused about total derivatives and partial derivatives.
My multivariable calculus book (Guidorizzi vol 2 Um Curso de Calculo) says that if I have a function like $f(a(u,v),b(u,v))$ then ...
2
votes
1
answer
3k
views
Lagrange equations in a conservative system, understanding $\nabla_i$
For a system of multiple particles with conservative forces: $\mathbf{F}_i = - \nabla_i V$, with $V \equiv V(\mathbf{r}_1,\dots,\mathbf{r}_N)$ the potential in function of the position of the $N$ ...
- 265
2
votes
2
answers
172
views
Conjugate momentum notation
I was reading Peter Mann's Lagrangian & Hamiltonian Dynamics, and I found this equation (page 115):
$$p_i := \frac{\partial L}{\partial \dot{q}^i}$$
where L is the Lagrangian. I understand this is ...
- 41
1
vote
2
answers
268
views
Why the $\Delta$ in the definition of pressure? (fluid mechanics)
I'm an engineering student (first year) studying Physics 1 (now an introduction to fluid mechanics).
Q1
In my physics textbook, the "medium pressure" is defined as:
$$p_m = \frac{\Delta F_{\...
- 141
1
vote
2
answers
123
views
Physics of small values and differentials
In some formulas in physics having a ratio, for example $ pressure={F \over\ A}$, the denominator is chosen to be a small quantity ($\Delta A$) and is written like,
$$P= {\Delta F\over \Delta A}.$$
...
- 151
1
vote
1
answer
412
views
What does lowercase-delta mean in Noether's first theorem?
Most expressions of Noether's Theorem I have come across do not use lowercase delta, but a couple sites do. I am confused....... Check out page 21 of the June 23 issue of 'Science News' ...
- 4,709
1
vote
1
answer
320
views
What is the meaning of $d$? [duplicate]
What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
user224451
1
vote
1
answer
164
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Question regarding Energy Interaction of two particles
https://i.sstatic.net/LUsKX.jpg
To give a context as to what I'm asking here ,I am talking about the energy of a two particle system (section 4.9 Taylor's Classical Mechanics) .
My question is what ...
- 367
0
votes
1
answer
57
views
What does this vertical line notation mean?
Here is the definition of the Noether momentum in my script.
$$I = \left.\frac{\partial L}{\partial \dot{x}} \frac{d x}{d \alpha} \right|_{\alpha=0} = \frac{\partial L}{\partial \dot{x}} = m \dot{x} = ...
- 85
0
votes
1
answer
134
views
Velocities - Equation 1.46 of Goldstein 3rd edition
In his derivation of the Euler-Lagrange equations from D'Alembert's principle, Goldstein
uses the parametrization (equation 1.45')
$$\displaystyle{\vec{r_i}=\vec{r_i}(q_1,q_2, ..., q_n, t)}\tag{1.45'}$...
- 113
0
votes
0
answers
359
views
Different subscripts for $\nabla$ operators while deriving force on system of many particles
Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system:
Total (external) force on ...
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