22 - Dynamics of Snowboating

Summary

Aims of the project

You are given a mathematical description of a winter sports area and invited to help design a run for the new winter sport of ‘snowboating’ – sliding down mountainsides in a rubber boat, more or less out of control. You will have to obtain reasonable model parameters to define safe operating conditions.

Mathematical ideas used

You are given a fairly realistic dynamical model based on Newton's laws. The equations of motion are coupled differential equations.

MATLAB techniques used

You can solve the differential equations using the numerical methods and MATLAB programmes of (Chapter 7). For convenience, there follows a list of relevant M-files, both standard ones and special ones provided for this particular project. You will have to modify some of these in the course of your study. In each case typing help gives information on the purpose and usage.

topog – 3D and contour plots of slopes

snows 1 – definition of the topographical surface

snowboat – solves the equations of motion for the snowboat

snbtfn – derivative function for the above

fsnow0 – surface function f (scalar args.)

fsnowl – fx and fy

fsnow2 – fxx, fxy and fyy

snowmn – minimisation function for the surface

snowmx – maximisation function for the surface

Preliminary look at the problem

Use the command topog to show a mesh plot followed by a contour plot of the snow hills where the action will take place. It is defined by

where f is some smooth function which can be examined in either snows1.m or fsnow0.m.