Computer Algebra Recipes

4.2. SECOND-ORDER MODELS 177
component is allowed to vary with z according to a hyperbolic cosine function.
The function Bz is taken to be constant inside the region z = ¡0:5 to0:5 and
allowed to grow linearly stronger outside this region.
> Br:=piecewise(z(t)>1,cosh(z(t)),z(t) Bz:=piecewise(abs(z(t)) B1:=subs(fx(t)=x,z(t)=z,y(t)=0g,B[1]):
B3:=subs(fx(t)=x,z(t)=zg,B[3]):
She uses the fieldplot command to represent the direction and magnitude
of the ¯eld with thick red arrows. A cross-sectional plot of the symmetrical
magnetic ¯eld is shown in Figure 4.8. Note that the size of the arrows is an
indication of ¯eld strength, bigger arrows for stronger ¯elds. The ¯eld con¯guration
shown in the ¯gure should allow magnetic bottle behavior.
> fieldplot([B3,B1],z=-1.5..1.5,x=-1..1,arrows=THICK,grid=
[15,15],color=red,scaling=constrained,tickmarks=[3,3]);
x
1
–1 0
1
z
–1
Figure 4.8: Magnetic ¯eld con¯guration to produce a magnetic bottle.
To animate the motion of a charge in her magnetic bottle, Vectoria chooses the
nominal mass and charge values m =1andq = 1 and the initial conditions