My Projects
Moisés Solorio
3D Visualization of ODE´s & solution curves
This worksheet helps visualizing the value of the derivative of a function as a 3d surface. It works only for ode´s of the form:
y(x)' = f (x,y)
being y the dependent variable, & x the independent var.
> with(plottools):with(DEtools): with(plots):
eq:=diff(y(x), x)=-y(x)*cos(x); #----enter the ODE (it's displyed)
limx:=-5..5: # ---------------the limits for x
limy:=-5..5: # ----------------the limits for y
sol:=dsolve(eq,
y(x)); # ----------------displays the solution
p1:=plot3d(rhs(eq),
x=limx, y=limy,lightmodel= 'light4',projection=.5,shading=ZHUE,axes=BOXED):
p3:=[seq(subs(_C1=i*.2,rhs(sol)),
i=-10..10)]:
p4:=plot(p3,x=limx,
color=black, thickness=2):
f
:= transform((x,y) -> [x,y,0]):
display({p1,f(p4)});
3D Visualization of Vectors
This worksheet helps visualize the interaction between time-dependent angular velocity, acceleration, tangential vel., accel. and the position vector ...as long as the angular acceleration is constant.
> with(VectorCalculus):
BasisFormat(true);
w:=<2*sin(t),cos(t),-sin(2*t)>;
r:=<cos(t),2*sin(t),t>;
CrossProduct( w, r
):
v:=simplify(%);
diff( v, t ):
a:=simplify(%);
vector w : Angular velocity ( 
)
vector r : Position vector
vector v : Linear velocity vector
vector a : Linear acceleration vector
> with(plots):
r1:=convert(w,list):
r2:=convert(r,list):
r3:=convert(v,list):
r4:=convert(a,list):
p1:=animate(spacecurve,[r1,t=0..A,
color=blue,labels=[x,y,z]], A=0..4*Pi, frames=50 ):
p2:=animate(spacecurve,[r2,t=0..A,
color=red,labels=[x,y,z]], A=0..4*Pi, frames=50
):
p3:=animate(spacecurve,[r3+r2,t=0..A,
color=green,labels=[x,y,z]], A=0..4*Pi, frames=50 ):
p30:=animate(spacecurve,[r4+r2,t=0..A,
color=black,labels=[x,y,z]], A=0..4*Pi, frames=50 ):
p4:=animate(arrow,[r1,
color=blue,labels=[x,y,z], width=1], t=0..4*Pi,frames=50 ):
p5:=animate(arrow,[r2,
color=red,labels=[x,y,z]], t=0..4*Pi, frames=50 ):
p6:=animate(arrow,[r2,r3,
color=green,labels=[x,y,z]], t=0..4*Pi, frames=50 ):
p60:=animate(arrow,[r2,r4,
color=black,labels=[x,y,z]], t=0..4*Pi, frames=50 ):
display([p1,p2,p3,p30,p4,p5,p6,p60],labels=[x,y,z]
,title=`V = w x r`,axes=boxed,scaling=constrained, projection=0.5);
r1:
vector function w : Angular velocity ( )
r2: vector function r : Position vector
r3: vector function v : Linear velocity vector
r4: vector function a : Linear acceleration vector