Modelling the movement and jumps of a chalk while drawing a dashed line on a blackboard

You probably know that if you try to draw a line using a piece of chalk on a blackboard , under some conditions (for example, $\alpha<\frac{\pi}{2}$ in the picture below) you will have a dashed line pattern instead of a continuous line.

My question is :

(how) Can you model this special movement of the chalk ,and specially , find the length of line segments and the distance between them(which are the visible characteristics of the motion)?

Note:gravity is present. (I think it affects the solution, at least in some models)

The pattern:

-
Well, the first thing I would do it figure out why that happens? It seems like the chalk gets stuck (doesn't overcome static friction). This strains the chalk, causing some stress to push against static friction. At some point the response to the strain overcomes friction and the chalk suddenly jumps to a new position. The distance would be given by how fast you are moving across the blackboard. –  levitopher May 7 '13 at 19:58
Similar dynamics to the ones @levitopher describes occur when bowing a violin string. This has been extensively modelled because of its applications in sound synthesis, so it might be worth looking into the literature surrounding that. (I'm not familiar enough with it myself to attempt an answer to this question.) –  Nathaniel May 8 '13 at 6:44
See a truly expert in action, here (Walter Lewin) –  Eduardo Guerras Valera May 10 '13 at 17:16