Equations of motion for a rotational system

Click For Summary
SUMMARY

The discussion focuses on deriving the Laplace transformed equations of motion for a rotational system, specifically addressing the confusion surrounding the rotational dynamics of a system with inertia J2. The participants highlight the importance of defining absolute rotations (phi1, phi2) instead of relying solely on the angles (theta1, theta2) to clarify the motion. This approach aids in understanding the contributions of torques to the equations of motion, particularly when J=0, and facilitates a clearer formulation of the system's dynamics.

PREREQUISITES
  • Understanding of Laplace transforms in control systems
  • Familiarity with rotational dynamics and inertia concepts
  • Knowledge of torque and its effects on motion
  • Basic principles of angular motion and equations of motion
NEXT STEPS
  • Study the application of Laplace transforms in mechanical systems
  • Explore the derivation of equations of motion for rotational systems
  • Learn about the role of torque in rotational dynamics
  • Investigate the implications of defining absolute rotations in complex systems
USEFUL FOR

Students and professionals in mechanical engineering, particularly those focusing on dynamics and control systems, will benefit from this discussion. It is also valuable for anyone involved in modeling rotational systems and analyzing their motion.

theone
Messages
81
Reaction score
0

Homework Statement


http://postimg.org/image/9fw7awqov/
The question is to write the Laplace transformed equations of motion for the system

Homework Equations

The Attempt at a Solution


I am confused about a couple of things: why is an angle is not defined for the rotation of J2. Does it means J2 does not have linearly independent motion?And the fourth equation of motion (for the second J=0), I can understand the theta 4 term being due to the torques associated with it's motion but I don't get the other term.
 
Physics news on Phys.org
I think I would suggest that you start by ignoring the thetas as defined, and simply define absolute rotations, phi1, phi2, etc. for each body. Then write the equations of motion. At that point, you will be in a better position to back into the equations you gave previously in terms of theta1, theta2, etc.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 35 ·
2
Replies
35
Views
5K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 32 ·
2
Replies
32
Views
3K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K