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Simple toys with complex behavior

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Traditional friction models slow down motion. No direction reversal ... Interesting results when bouncing between floor and underside of table. ... – PowerPoint PPT presentation

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Title: Simple toys with complex behavior


1
(No Transcript)
2
  • Simple toys with complex behavior
  • High friction between rubber and floor causes the
    ball to spin after impact
  • Traditional friction models slow down motion
  • No direction reversal
  • Solved by introducing a horizontal coefficient of
    restitution

3
  • A point object is insufficient to model the ball
  • Points have no angular momentum
  • Horizontal velocity never changes
  • Vertical velocity simply reverse of impact
    velocity scaled by vertical coefficient of
    restitution
  • Spin is what makes the ball interesting
  • Affects the slip velocity at point of impact

4
  • Model the ball as a rigid sphere
  • Slip velocity depends on horizontal and angular
    velocities
  • Slip velocity can be greater or less than
    horizontal velocity, or even opposite direction

Velocity components at impact
5
  • Angular momentum is conserved about impact point
    P since both impact forces go through P
  • Separate equations of motion into free fall and
    impact
  • Use 3-1-2 Euler angles to avoid singularity at
    initial condition (all Euler angles 0)

6
  • Free fall equations just gravity
  • Impact equations
  • new vertical velocity
  • original slip velocity
  • new slip velocity

7
  • Impact equations (continued)
  • New horizontal velocity and angular velocity
  • Depends on new slip velocity
  • And conserved angular momentum about P
  • Break into component equations and solve for new
    horizontal and angular velocities
  • Simulation numerically integrate between impacts
    using freefall equations

8
  • Interesting results when bouncing between floor
    and underside of table.
  • Spin impact causes changes in direction depending
    on whether the spin is with or against the
    horizontal velocity
  • The slip velocity adds and subtracts from the
    horizontal velocity on opposite sides of the ball

9
  • No friction horizontal e -1

10
  • Sticky impact horizontal e 0

11
  • Complete reversal horizontal e 1

12
  • Spin, gravity, vertical e lt 1, horizontal e 1

13
  • Side spin, gravity, vertical e lt 1, horizontal e
    1

14
  • Questions?
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