All Questions
24
questions
0
votes
2
answers
74
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Energy in different coordinates in central force motion
With reference to central force, we see that K.E has 2 terms in 2D cartesian cordinate but just 1 term in polar coordinates and potential energy has 1 term in cartesian but 2 terms in polar.
Basically ...
- 367
1
vote
1
answer
49
views
How do physicists determine where to place the world or inertial frame when describing the equation of motion of an object?
For example, I have a pendulum as shown in the diagram above. I would like to write down its equation of motion. To do this, I must define a world frame (or inertial frame, or origin).
But this is ...
- 320
1
vote
0
answers
36
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How do 4-vectors change under an "accelerated" Lorentz transformation?
I assume that an observer moving with velocity $\mathbf{v} = v\mathbf{n} = \mathbf{v}(t)$ (with respect to another observer) has coordinates
where $x^{\mu}$ are the coordinates for the observer who ...
- 391
0
votes
2
answers
119
views
Question about velocities in different reference frames
Suppose $\hat{x^{'}}, \hat{y^{'}}, \hat{z^{'}} $ are the unit vectors of an inertial frame and $\hat{x}, \hat{y}, \hat{z} $ are the unit vectors of a frame which maybe accelerating, rotating, whatever....
- 430
0
votes
1
answer
68
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Doubt in fictitious forces chapter in Morin
The question is this -
I know 2 is what the non-inertial frame measures, but isn't $\frac{d\mathbf{A}}{dt}$ the real thing, the physical thing? And you can write that too in terms of the unit vectors ...
- 430
0
votes
1
answer
44
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In terms of which zero should i calculate the potential energy in the Lagrangian formalism?
What I understand is that we have two kinds of coordinates when working with the Lagrangian formalism with different zeros (which may happen to coincide) to measure from, those are the Cartesian ...
- 959
1
vote
2
answers
334
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Frames of references and coordinate systems
In linear algebra, a vector can be represented by different bases. However, this is merely a different representation of the same entity; i.e. $\vec x = x\hat\imath + y\hat\jmath + z\hat k = x'\hat\...
- 27
0
votes
2
answers
520
views
Decomposing Lagrangian into CM and relative parts with presence of uniform gravitational field
Most problems concerning two-body motion (using Lagrangian methods) often only consider the motion of two particles subject to no external forces. However, the Lagrangian should be decomposable into ...
- 343
5
votes
3
answers
437
views
Passive transformation, pseudo vectors and cross product
Let's consider the passive transformation i.e. inversion only of the basis vectors (coordinate axes) and all other vectors remaining the same and check if the cross product is a pseudo vector.
After ...
- 1,260
5
votes
7
answers
2k
views
Why can basis vectors change direction?
I thought that basis vectors were of magnitude one and located at the origin and were each linearly independent, so how in things like polar coordinates can the basis vectors be moving?
- 139
0
votes
1
answer
48
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The E-L equations in a non-inertial frame
These are from pages 126 and pages 127 about the subject, (EDITED: from L&L A course of theoretical physics) but I don't really get one thing.
"Thus an accelerated translational motion of a ...
- 15
8
votes
9
answers
2k
views
Different coordinate system as opposed to different reference frame
I'm having a hard time getting the difference between the two. In Euler's equations of rotating bodies for example, we have:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
- 1,028
0
votes
2
answers
154
views
Generalized coordinates as components
Why we cannot express Generalized coordinates as a vector like we do with Cartesian coordinates $x$ , $y$ ,$z$ ?
- 11
4
votes
4
answers
542
views
Is the numerical value of the Lagrangian conserved, when moving between inertial reference frames?
I am doing a course on Lagrangian mechanics and the instructor mentioned that the numerical value of the Lagrangian is conserved when I shift between two inertial reference frames, even though their ...
- 593
1
vote
0
answers
376
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Rewriting the Lagrangian in terms of the constant(s) of motion doesn't work. Why? (spherical pendulum) [duplicate]
I am trying to solve for the equations of motion to simulate a spherical pendulum. I decided to use the spherical coordinates. The Lagrange equation is,
$$
L=T-V=\frac{1}{2}m\left(l\dot\theta\right)^2+...
- 317