All Questions
156
questions
5
votes
1
answer
423
views
Curvilinear Coordinates and basis vectors
In these notes,
$\frac{\partial \vec{r}} {\partial q_i}$ is stated to form a basis set for the vector space. How does this happen?
Also, how does one justify this equation from Goldstein's ...
- 1,578
7
votes
2
answers
3k
views
Covariance of Euler-Lagrange equations under change of generalized coordinates
Suppose I have an inertial frame with coordinate $\{q\}$. Now I define another reference frame with coordinate $\{q'(q,\dot q,t)\}$. I obtain the equation of motion in $\{q'\}$ in two different ways:
...
- 4,014
9
votes
1
answer
3k
views
Point of Lagrange multipliers
I am trying to understand how for a constrained system the introduction of Lagrange multipliers facilitates the incorporation of the holonomic constraints. I am using Classical Mechanics by John ...
- 187
7
votes
2
answers
3k
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How do you derive Lagrange's equation of motion from a Routhian?
Given a Routhian $R(r,\dot{r},\phi,p_{\phi})$, how do you derive Lagrange's equation for $r$? Do you just solve the following for $r$?
$$\frac{d}{dt}\frac{∂R}{∂\dot{r}}-\frac{∂R}{∂r}=0.$$
And as a ...
user27771
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
9
votes
5
answers
2k
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Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system?
I am a Physics undergraduate, so provide references with your responses.
Landau & Lifshitz write in page one of their mechanics textbook:
If all the co-ordinates and velocities are ...
- 840