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Results tagged with classical-mechanics
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user 256066
Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].
2
votes
2
answers
334
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About virtual displacement
Thornton Marion
The varied path represented by $\delta y$ can be thought of physically as a virtual displacement from the actual path consistent with all the forces and constraints (see Figure above …
CommunityBot
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1
vote
1
answer
513
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Virtual displacement for a block sliding down a wedge
A block slides on a frictionless wedge which rests on a smooth horizontal plane. There are two constraints in this system. One that the wedge can only move horizontally and another that the block mus …
CommunityBot
- 1
6
votes
3
answers
912
views
Angular momentum of a purely rotating body about any axis
It's proved in my K&K mechanics textbook that in pure rotation about an axis passing through the body it's angular momentum is $I\omega$.
What about if I want to find the angular momentum about an ax …
8
votes
3
answers
4k
views
Non-uniqueness of the Lagrangian
Goldstein, 3rd ed
$$
\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q}_{j}}\right)-\frac{\partial L}{\partial q_{j}}=0\tag{1.57}
$$
expressions referred to as "Lagrange's equations."
Note that fo …
2
votes
2
answers
108
views
Help in understanding this derivation of Lagrange Equations in Non-Holonomic case
Whittaker, Analytical dynamics pg 215
I don't understand how we get the final equations relating $Q_r$ with $\lambda$ given the conditions above?
- 213k
0
votes
1
answer
105
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Virtual work of constraints in Hamilton‘s principle
Goldstein 2ed pg 36
So in the case of holonomic constraints we can move back and forth between Hamilton's principle and Lagrange equations given as $$\frac{d}{d t}\left(\frac{\partial L}{\partial \do …
- 213k
0
votes
2
answers
444
views
Energy conservation equation for an object rolling up an incline [closed]
An sphere of radius $R$ rolls up an incline. We can write mechanical energy conservation equations for this motion because neither does the normal or the frictional force do any work.
At the top of th …
- 10.4k
0
votes
1
answer
192
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What is 3-force in special relativity?
We define 4-force as one which satisfies: $\mathbf{f}=m \mathbf{a}$ where $\mathbf{a}=\frac{d \mathbf{u}}{d \tau}$.
The quantities in bold face are 4-vectors.
Hartle pg 88 defines a 3-force as:
$\frac …
- 213k
1
vote
1
answer
819
views
Conservation of angular momentum using symmetry properties
Goldstein pg 59
It can be shown that if a cyclic coordinate $q_{j}$ is such that $d q_{j}$ corresponds to a rotation of the system of particles around some axis, then the conservation of its conjugat …
CommunityBot
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0
votes
4
answers
751
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Transformation equations from Generalized coordinates to rectangular
I've a proper set of generalized coordinates {$q_j$} ,$j=1...n$ for a system. This set determines the configuration of the system, also these can be used to determine the rectangular coordinates of al …
- 2,566
2
votes
2
answers
167
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A doubt in a Wikipedia article discussing Bertrand's theorem
Wikipedia while deriving Bertrands theorem writes after some steps:
...For the orbits to be closed, $β$ must be a rational number. What's more, it must be the same rational number for all radii, sinc …
- 5,421
0
votes
2
answers
92
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Why is this matrix symmetric?
Goldstein 3rd Ed, pg 339
In large classes of problems, it happens that $L_{2}$ is a quadratic function of the generalized velocities and $L_{1}$ is a linear function of the same variables with the fo …
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votes
0
answers
65
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Form of potential $V$ for conservative forces
Goldstein, Pg 21,3rd E.d writes
only if $V$ is not an explicit function of time is the system conservative
That means $V(r,\dot{r})$ is a conservative potential, however I think that only potentials …
- 213k
0
votes
1
answer
243
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Why Polhode is a circle in a symmetric body
Goldstein
In the special case of a symmetrical body, the inertia ellipsoid is an ellipsoid of revolution, so that the polhode on the ellipsoid is clearly a circle about the symmetry axis. The herpol …
- 12.8k
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vote
0
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"Inertia tensor possess a type of revolution about Centre of mass" ? Can't understand this s...
Goldstein pg 194, 3rd Ed.
$$
T_{\text {rotation }}=\frac{1}{2} I_{\alpha \beta} \omega_{\alpha} \omega_{\beta}
$$
where
$$
I_{\alpha \beta}=m_{i}\left(\delta_{\alpha \beta} r_{i}^{2}-r_{i \alpha} r_{ …
- 1,330