Lab · Engineering Mechanics
Rigid-Body Dynamics Lab
A planar rigid body driven by constant global forces applied at body-fixed points and by free couples. Force components stay fixed in the inertial frame while their application points turn with the body, so an eccentric load can change the moment about G as the body rotates.
Model
Numerical solutionAt least one force has a lever arm. Its application point turns with the body while its direction stays fixed, so M_G varies with orientation and the motion is integrated with a fixed-step RK4 scheme.
Body and initial state
A mass moment of inertia about G, not an area second moment.
Loads
Forces
Components are global and constant; the application point is body-fixed, given as an offset from G in the body frame.
Couples
A couple is positive counter-clockwise and has no application point, so it never changes the resultant force. The symbol coordinates are body-fixed and move the drawn arc only: the motion, the accelerations, the energy and the momentum are unchanged.
Workspace
The cursor reads one computed sample. It re-integrates nothing and stays out of the shared link.
Free-body diagram at the cursor
- Name
- R = ΣF
- Magnitude
- 10 N
- Direction
- 90°
- Components
- (0, 10) N
- Application point
- (0, 0) m
Load reduction and equations of motion
| Orientation θ | 0° (0 rad) |
|---|---|
| Resultant force R = ΣF | (0, 10) N |
| |R| | 10 N |
| Moment about G, ΣM_G | 10 N·m |
| Acceleration a_G = R/m | (0, 5) m/s² |
| Angular acceleration α = ΣM_G/I_G | 2.5 rad/s² |
| Moment of F1 about G at θ₀ | 10 N·m |
Moments are positive counter-clockwise and taken about the centre of mass.
What this Lab models
Finds the planar motion a rigid body undergoes under constant global forces at body-fixed points and free couples, from ΣF = m·a_G and ΣM_G = I_G·α — the motion caused by loads, the inverse of the Rigid-Body Kinematics Lab, which describes a motion without asking what caused it.
Related calculations
Continue
The pose and the rates at the cursor become a prescribed-acceleration model, so the point velocities and the instantaneous centre can be examined at that instant.