When investigating mechanical problems it is often more convenient to deal with scalars rather than vectors. In this project methods stemming from the field of analytical mechanics, which lets one derive the equations of motion using scalar quantities instead of vectors, have been used. Two mechanical problems were investigated, a double pendulum with a spring and particles orbit in a sphere. The equations of motion of the two systems were derived with the assistance of computer algebra, using Maple and the external package Sophia. The systems were investigated with regard to periodicity and conserved quantities..

In this project we have used the theory of analytical mechanics to derive equations of motion for complex mechanical systems in order to study their behaviour over time. Even if the theory provides powerful tools to tackle tough problems which would be very hard to solve by methods of Newtonian mechanics, you are still relatively limited without running any computer simulations. One realises that in a faster rate it will be an incredibly difficult task to find an analytical solution when the degrees of freedom increases. Even if one would succeed to derive the equations, one still has to solve them to get the information of the systems behavior. Of experience one knows that the equations in general are nonlinear and hence must be integrated numericaly.

SammanfattningSkolverket beslutade 2006 att tillåta symbolhanterande räknare på nationella prov i matematik för alla gymnasieelever från höstterminen 2007. Beslutet debatterades flitigt t.ex. i tidskriften Nämnaren.Prototypen till en ny symbolhanterande räknare testades i sju ?pilotklasser? vid fyra svenska gymnasieskolor från december 2006. Jag har följt två av dessa klasser t.o.m.