All Questions
26
questions
1
vote
1
answer
403
views
What is the degrees of freedom (Lagrange equation) of two connected spool rolling down two inclines?
I'm quite confused as to how to use the Lagrange equation [second type] in a system which features a spool rolling down an incline. I think this particular example is quite representative of what is ...
CommunityBot
- 1
0
votes
1
answer
1k
views
Lagrangian Mechanics - Bead sliding on a rotating rod
Say I have a bead of mass $m$ sliding on a friction-less rod (or wire) that is rotating with a permanent angular velocity $\omega$. The whole system is under the influence of a uniform gravitational ...
CommunityBot
- 1
3
votes
2
answers
243
views
Locally accessible dimensions of configuration space
I am reading a book called "Structure and Interpretation of Classical Mechanics"
by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following:
Strictly ...
CommunityBot
- 1
0
votes
0
answers
19
views
Precise Definition of Degrees of Freedom [duplicate]
I am taking Analytical Mechanics and while reading Goldstein's and LL something bothered me: can I say that a degree of freedom is an independent (generalized) coordinate?
What bothers me is that we ...
- 207k
0
votes
1
answer
781
views
Degrees of freedom for Constrained Motion
I'm starting to learn about Degrees of freedom, and the idea of 'constrained motion' seems strange to me, surely any particle with a predefined path is 'constrained' in its motion, We also had ...
CommunityBot
- 1
5
votes
2
answers
1k
views
Why can we assume independent variables when using Lagrange multipliers in non-holonomic systems?
I'm studying from Goldstein's Classical Mechanics, 3rd edition. In section 2.4, he discusses non-holonomic systems. We assume that the constraints can be put in the form
$$f_\alpha(q, \dot{q}, t) =0, ...
- 227
0
votes
0
answers
69
views
How many DOF does this system have?
I saw the problem above and thought it would be fun to solve it using lagrangians. However, in order to do this, one has to know the DOF of the system. And this is where it gets confusing for me. ...
- 207k
3
votes
3
answers
4k
views
Degree of freedom in Lagrange's formalism
Degrees of freedom $=3K-N$ where $K$ is number of particles and $N$ is number of constraints. How to find the number of degrees of freedom for a rigid body which has both translation and rotation, ...
CommunityBot
- 1
4
votes
1
answer
413
views
Why are $p$ and $q$ independent variables in Hamiltonian formalism?
Let's say we have $(q, \dot{q})$ as the generalised coordinate and generalised velocity. If we have a Lagrangian given by
$$L=Aq\dot{q}+Bq$$
where $A$ and $B$ are constants that give the right units ...
- 207k
1
vote
3
answers
184
views
Why should degrees of freedom be independent?
To define the position of a system of $N$ particles in space, it is necessary to specify $N$ radius vectors, i.e. $3N$ co-ordinates. The number of independent quantities which must be specified in ...
- 7,514
1
vote
3
answers
221
views
Why not a $(q,\dot{q})$ space in Lagrangian Mechanics?
We know that the Lagrangian $\mathcal{L}(q,\dot{q},t)$ which is function of generalized co-ordinate, generalized velocity and time. We consider the dynamics of particle is in configuration space. But ...
- 207k
1
vote
0
answers
93
views
Representation of Holonomic Constraints by independent generalized coordinates
Say we have a system with N particles described by N position vectors: $\{\vec{r_{i}}\};$ $i=1,...N$
Say we have a holonomic constraint: $$f(\{\vec{r_{i}}\},t)=0 \tag{1}$$
Since we have one holonomic ...
- 207k
2
votes
0
answers
141
views
Understanding the Degrees of freedom of a Ballbot
A Ball Balancing Robot is dynamically stable robot capable of omnidirectional motion. It possesses non-holonomic properties and is a special case of underactuated system, classified as a Shape-...
- 71
4
votes
0
answers
281
views
Pendulum constrained by a spring and generalized forces [closed]
I've been going through some problem sets used in a classical mechanics course offered a few semesters ago as a way to prepare for when I have to take that course next semester and I've hit a snag ...
- 2,646
5
votes
1
answer
456
views
How can one modify the Nambu-Goto action to include the longitudinal degrees of motion?
The Nambu-Goto action is given by
$$ S = -\frac{T_0}{c} \int_{-\infty}^{+\infty} d\tau \int_{0}^{\sigma} d\sigma \sqrt{ \Bigg(\frac{\partial X^\mu}{\partial \tau} \frac{\partial X_\mu}{\partial \...
- 8,492