Tagged Questions
0
votes
0answers
33 views
Lagrangian with a general constraint [closed]
Can any body help me out to solve this problem?
I am familiar with mechanism of Lagrangian and I can solve some problems with constraints but this one is really hard to solve.
1
vote
1answer
104 views
Euler-Lagrange for constrained system
Suppose we have Euler-Lagrange system with generalized coordinate $r_1$ and $r_2$, and input $u_1$ and $u_2$. I know how to prove this system is indeed Euler-Lagrange system.
Suppose now if we have a ...
3
votes
2answers
88 views
How is the physical Lagrangian related to the constrained minimization Lagrangian?
If we're minimizing an energy $V(q)$ subject to constraints $C(q) = 0$, the Lagrangian is
$$L = V(q) + \lambda C(q).$$
I have fairly solid intuition for this Lagrangian, namely that the energy ...
3
votes
3answers
201 views
Writing $\dot{q}$ in terms of $p$ in the Hamiltonian formulation
In the Hamiltonian formulation, we make a Legendre transformation of the Lagrangian and it should be written in terms of the coordinates $q$ and momentum $p$. Can we always write $dq/dt$ in terms of ...
2
votes
5answers
320 views
How are constraint forces represented in Lagrangian mechanics?
Suppose we try to obtain the movement equation for a particle sliding on a sphere (no friction, ideal bodies...). The only forces acting on the particle are its weight and - here's my problem - a ...
8
votes
4answers
231 views
What makes an equation an 'equation of motion'?
Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint.
For example, in the ...
1
vote
1answer
150 views
A particular case when Lagrange equation is equivalent to equation of motion on a Riemannian manifold
Suppose a particle is moving on a surface of a sphere,then it contains a holonomic constraint and so the three Cartesian co-ordinates are available with a constraint equation(equation of surface in ...
3
votes
1answer
388 views
When is the principle of virtual work valid?
The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints.
Goldstein says something I don't understand. He says ...
3
votes
1answer
128 views
Showing constraint is nonholonomic
One example of a nonholonomic constraint is a disk rolling around in the cartesian plane that is constrained to not be slipping.
These leads to the constraint $dx - a \sin\theta d\phi = 0$ and $dy - ...
7
votes
2answers
204 views
Why so many arguments for the transformation equations of generalized coordinates?
For a system of $N$ particles with $k$ holonomic constraints, their Cartesian coordinates are expressed in terms of generalized coordinates as $$\mathbf{r}_1 = \mathbf{r}_1(q_1, q_2,..., q_{3N-k}, ...
