Formulation rigid body constraint

  • Thread starter Larsen1000
  • Start date
  • #1
Larsen1000
2
0
Hello

I need some help with formulating the constraint force for a sliding and rotating box. The scenario is: A box is sliding down a slanted table. The center of gravity has passed the edge of the table so the box receives a counter force and torque.

I am solving the forces and moments which acts through center of gravity and therefore have formulated:

Fn = -(gravity * Rotation matrix *Constraint vector) - (Forces from external moments and rotational velocity)

The constraint vector is [0 1] which eliminates tangent forces at the edge and leaves the normal force. The point where I have problems is to formulate the constraint force caused by the rotational component. Can someone help me with this?
 

Attachments

  • Constraint Force.png
    Constraint Force.png
    1.8 KB · Views: 398

Answers and Replies

  • #2
K^2
Science Advisor
2,470
32
Are you trying to approach this from Lagrangian formalism or Newtonian formalism? For the later, you don't need the angular component. Just solve for normal force that gives normal acceleration = 0, and then substitute that along with point of contact for torque. The force will depend on angle, but not on angular velocity.

For Lagrangian formalism, you only need the constraint equation. Easiest way to get that is to take coordinate of the CoM to be (x,y) and of the contact point (0,0). Then you trivially get ycosθ-xsinθ=h/2 as your constraint equation, where h is the height of the brick and θ corresponds to brick laying flat on horizontal surface.

Of course, you need to keep in mind that at some point the brick will separate. Watch for Fn changing sign.
 

Suggested for: Formulation rigid body constraint

Replies
3
Views
350
  • Last Post
Replies
8
Views
710
Replies
2
Views
302
Replies
8
Views
606
Replies
1
Views
601
  • Last Post
Replies
2
Views
333
Replies
1
Views
263
  • Last Post
2
Replies
61
Views
2K
Replies
10
Views
445
  • Last Post
Replies
2
Views
489
Top