All Questions
24
questions
8
votes
3
answers
741
views
In a general physical sense, is the position of a particle really a vector?
Is it consistent to define the position of a particle in some frame as a vector or is just an informal representation? Velocity and acceleration can be added up and multiplied by real numbers and ...
- 1,290
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:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
- 1,038
7
votes
2
answers
5k
views
Centrifugal Force and Polar Coordinates
In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
- 115
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
5
votes
3
answers
446
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 ...
- 1,270
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
4
votes
5
answers
702
views
Why we use vectors?
When we say that the position of an object is +5m on x axis why we need to use vectors? I mean could we don't use vectors and just say +5m on x or y or z axis instead of writing 5*unit vector either $...
- 1,648
3
votes
4
answers
675
views
Understanding the definition of tangent basis
This question could sound silly but I though a lot about it and I'm not new to physics.
Let's say I have a plane on which I use polar coordinates, it means a point $P$ can be indicated by its ...
- 1,904
2
votes
1
answer
675
views
Possible error in Marion and Thornton's Classical Dynamics of Particles and Systems
I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3
The rotation matrix associated with 1.2a and 1....
- 43
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
2
answers
1k
views
Do rotation matrices rotate about inertial or body angles? [closed]
I have Yaw, pitch, and roll angles in that order (Euler 321) to apply to a body reference frame in cartesian coordinate system. I want to know what the body reference frame vector coordinates are ...
- 995
1
vote
0
answers
36
views
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
1
vote
0
answers
378
views
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
1
vote
1
answer
83
views
Doubt on the difference between a rotational coordinate system and spherical coordinate system and the calculation of the Christoffel sysmbols
I know basic differential geometry for general Relativity and classical mechanics. But an interesting fact was revealed in my calculations, namely, that I discovered that I didn't realize the ...
- 3,085
1
vote
2
answers
337
views
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