All Questions
24
questions
1
vote
1
answer
83
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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
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
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
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
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
0
votes
1
answer
82
views
Question regarding the definition of generalized coordinates
In Classical Mechanics, John R. Taylor defines generalized coordinates like so:
Consider now an arbitrary system of $N$ particles, $\alpha = 1, \dots , N$ with positions $\boldsymbol{r}_a$. We say ...
user113773
0
votes
1
answer
2k
views
Significance of centrifugal potential
While dealing with central forces (purely using newtonian mechanics) I've came across this result:
$$U_\text{eff}(r)=\frac{l^2}{2\mu r^2}+ U(r) \, .$$
I'm not at all fluent with the lagrangian ...
1
vote
2
answers
1k
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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
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