All Questions
14
questions
2
votes
1
answer
89
views
Time derivative of a "general" vector $\vec A$ in an accelerating frame: what about e.g. velocity $\vec v$?
According to Morin "Classical Mechanics" (Section 10.1, page 459), the derivative of a general vector $\vec A$ in an accelerating frame may be given as
$$\frac{d\vec A}{dt}=\frac{\delta \vec ...
- 23
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
views
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
91
views
On the isomorphism between directed line segments and "abstract vectors" (Gregory Classical Mechanics)
I have just begun reading Gregory's Classical Mechanics and, amazingly, he has blown my mind in the first chapter discussing nothing more than measly old vector algebra. Fascinating that Gregory was ...
- 1,095
2
votes
1
answer
258
views
Having trouble deriving the exact form of the Kinematic Transport Theorem
The Kinematic transport theorem is a very basic theorem relating time derivatives of vectors between a non rotating frame and another one that's rotating with respect to it with a uniform angular ...
- 1,417
1
vote
1
answer
91
views
How to define differentiation of a time-dependent vectors with respect to a specific reference frame in a coordinate-free manner?
It is usual in classical mechanics to introduce the derivative of a time-dependent vector with respect to a reference frame. This is accomplished through the use of a basis that is fixed with respect ...
- 245
1
vote
2
answers
334
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
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
57
views
Dummy variables and Galilean Invariance
I've faced a small doubt, and I was hoping someone could verify this for me.
According to Galilean transformation, consider $2$ frames - $S_1$ and $S_2$ moving relative to each other. $S_1$ is at rest,...
- 1,771
1
vote
2
answers
185
views
Resolution of vectors along different directions
I have a small doubt regarding the resolution of forces and vectors.
Suppose, we have our standard cartesian coordinate system, with unit vectors $\hat{i}$ and $\hat{j}$. Now we have defined polar ...
- 1,771
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
8
votes
3
answers
735
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
4
votes
5
answers
697
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