A Bee spiraling in to a Hive

Description : A bee is going to start at some radial distance from the origin with an initial radial velocity/acceleration. We will also give the bee an initial angular velocity and acceleration. In both cases, we confine ourselves to no more than a quadratic relationship between the position/angle and time:
                                           theta = theta0 + omega0*t + ½*alpha*t2
                                           r = r0 + vr0*t + ½*ar*t2
The angle theta is positive in a clockwise sense. The angle is measured out from the hive (the origin), and the radius vector points to a point P on the path (indicated in the animation). The vectors coming out of the red point P are the blue instantaneous velocity vector (scaled down by a factor of 4), and the green instantaneous acceleration vector (scaled down by a factor of 20). You can change the various values below, and then click the Update Information button, and then the PLAY button to run the animation.

Initial conditions :

  • Initial angle (theta0) of the Bee  radians
  • Initial anglular velocity of the Bee  rad/s
  • Angular acceleration of the Bee  rad/s/s
  • Initial radial position (r0) of the Bee meters
  • Initial radial velocity (out=+) of the Bee  m/s
  • Radial acceleration (out=+) of the Bee  m/s/s

Stop when Bee finds the Hive? or
Stop at this time : seconds.

Show Bee image?

Message from the Bee :

Horizontal plotting constraints :
Variable plotted : time    Theta    Theta/Pi    X
Autoscale Horizontal or
My scale : HorMin =   HorMin =

Vertical plotting constraints :
Variable plotted : X   Y   r   |V|   |A|   Vrad   Vang   Arad   Aang
Autoscale Vertical or
My scale : VerMin =   VerMin =

(The animation may move off screen, but the graph will go until you stop it.)

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