The purpose of the simulation videos presented here is to analyze multibody systems in simultaneous, indeterminate contact and impact with friction. The theory and unique approach developed during my thesis and dissertation work is applied and the results obtained are displayed below.



    Analytic approach: frictionless, e* = 1 (created 02/20/13)


    Analytic approach: frictionless, e* = 0.85 (created 02/20/13)
Newton's Cradle: Three ball
Newton's cradle is a popular benchmark example analyzed because it is a multibody system with simultaneous collisions. In this simulation, the system consists of three balls of equal radius R and equal unit mass. The balls hang from massless strings of length L which are equally separated by a distance 2R, such that there is no separation and the balls are in contact at rest.





    Analytic approach: frictionless (created 05/20/13)


    Analytic approach: with friction (created 05/20/13)


    Optimization approach: with friction (created 11/28/11)
Rocking Block
The phenomena of interest for this example involves the transfer of energy between two points on a block, one in contact and one experiencing impact. Impact is associated with an abrupt change in velocity, while contact is assumed to be a long term interaction between surfaces. In these simulations, when a point impacts the surface it sticks to it, the coefficient of restitution equals zero; however, a point in contact is free to separate fron the surface. This type of simulation has been pursued by other researchers in relation to investigating the effects of earthquakes on buildings.

- Static and dynamic coefficients of friction were 0.5 and 0.35, respectively, for all impacting surfaces
- Width b and height h, where the ratio of b to h is less than the square root of 2 (flat block [C. Yilmaz, et al. 2009, B. Brogliato, et al. 2012])




    Optimization approach: with friction (created 10/14/11)
3D ball Impacting a Corner
This video shows a 3D ball impacting a corner. The ball impacts all three surfaces simultaneously, where sticking and slipping at the impact points is considered in the simulation. The three simultaneous impacts yield a model that is indeterminate with respect to the impact forces. These forces are resolved by enforcing the rigid-body relationship between the post-impact velocities at each impact point. The red asterisks on the ball indicate the three simultaneous impact points.




    Optimization approach: with friction (created 11/24/10)
2D ball Impacting a Corner
This video shows a 2D ball impacting a corner. The ball impacts both surfaces simultaneously and sticking and slipping at the impact points is considered in the simulation. The simultaneous impacts yield a planar model that is indeterminate with respect to the impact forces. These forces are resolved by enforcing the rigid-body relationship between the post-impact velocities at each impact point.