All Questions
Tagged with constrained-dynamicsrotational-dynamics
17 questions
3votes
2answers
308views
A question related to torque at the molecular level
My argument is: When you nudge the molecule at the end of a rigid body, that molecule must move in a straight line initially in order to transfer force to the pivot. However, due to Pythagoras’ ...
3votes
2answers
290views
What are the constraints of rolling without slipping on a rotating disk?
Given the following system: a disk rotating with constant angular velocity and a ball rolling without slipping on the disk. Imagine three diferent reference frames, $S, S', S''$. The $S$ frame is ...
- 1,821
0votes
1answer
83views
About the generalized coordinates of a pure rolling disc on a 2D plane being holonomic vs. semi-holonomic
This particular question is from eq. (1.39) in Goldstein "Classical mechanics". I've seen 2 kinds of solutions for a pure rolling disc on a 2D plane (i) using "differential 1-form"...
-5votes
1answer
105views
Predicting the position of a particle in spherical motion given two prior positions [closed]
I'm working on a problem involving a particle moving in 3D space under the following constraints: a. The particle maintains a constant distance R from the origin (moves on a sphere) b. There is no ...
0votes
3answers
116views
Rigid body constraint
While going through the rigid body constraint, I encountered the following statement: For two rigid bodies to remain in contact, the relative velocity of the contact points on both the bodies along ...
0votes
2answers
114views
Rolling ball on a surface with friction
For a point particle moving on a surface under the infuluence of gravity, the equation of motion is very easy to write down - the force on the particle is simply the projection of its weight $mg\...
- 1,131
2votes
1answer
50views
Equivalent Characterizations of Rigid Bodies & Angular Velocity Interpretation
In rotational kinematics, there seem to be two common characterizations of a rigid body: A rigid body is any collection of particles with position vectors $\textbf x_1,\textbf x_2,...$ such that the ...
3votes
4answers
261views
Rigid bodies: proof of existence of internal forces that preserve the distances [duplicate]
I am new to Physics and I have a pure Math background. I am currently studying mechanics and I have the following question regarding rigid bodies. I am posting here the 2D version of the question. If ...
- 242
0votes
2answers
309views
Constraint force that keeps a body in a circular path with fixed radius
I'm trying to simulate a simple electric motor from scratch. In order to do this I need to be able to apply forces to a body which can only travel around a circular parth, a rotating magnet. If my ...
- 3
0votes
0answers
128views
Question on non-holonomic constraints (This is different to the others)
I know there are many posts on non-holonomic constraints and also many on this exact one but I feel that there is still some confusion on it. "Consider a disk which rolls without slipping across ...
- 317
0votes
1answer
90views
Is there something like acceleration constraint in a rigid body? [closed]
Suppose we have two points on a body which having acceleration a1 and a2 direction we know and magnitude as well , is there some sort of relation between them we can establish , like for velocities ...
- 530
1vote
0answers
876views
Proof of holonomic constraints for a wheel on a track
I'm faceing a problem of a thin wheel of radius R rolling without slipping on a track (y = f(x); on xy-plan). The wheel plane stays vertical and tangent to the track at the contact point P. $\alpha$ ...
- 11
1vote
2answers
1kviews
Work done by constraints on rotating rigid bodies
I am trying to understand why constraint forces do no work on extended, rotating bodies. For instance, consider the problem of a rigid rod falling on a frictionless surface (K&K 7.17) There are no ...
- 838
1vote
1answer
998views
Find the acceleration of the bead [closed]
Two identical, uniform large rings, each of mass $\text{m}$ are connected through a bead of same mass, which can move freely. When bead is released, it starts sliding down. The large rings roll over a ...
- 252
0votes
1answer
416views
Build rotational Hamiltonian based on Lagrangian of general form
I've been told that one could build rotational Hamiltonian based on Lagrangian of general form: $\mathcal{L} = \mathcal{L} (\vec{\Omega})$. By introducing Euler angles one could rewrite Lagrangian in ...
