Hi, I am working on an assignment and I am having difficulties with this Eurler method since I am working with vector.
If the aircraft's engine transmits power P to the air, the force of the propellar, Fp, satisfies P=Fpv. Since the force Fp acts in the direction of motion, it can be written in vector form as: (what I have so far)
v:=Vector(2,1,[vx,vy]); velocity vector
nu:=v->Norm(Vector(v),2); (length of v)
Fd:=-1/2*C*rho*A*nu*v # air resistance
Fl:=1/2*Cl*rho*A*nu*v # liftforce in y direction here v=[-vy,vx]
Fp:=(P/nu^2)*v^2 # power from aircraft
All this adds up to:
F_T:=v->Vector(evalm(Fp/nu(v)^2*v+Fd*nu(v)*v+Fl*nu(v)*zip((x,y)->x*y,v([2,1]),Vector([-1,1]))+Vector(2,1,[0,-m*g]))); # I have tried it and it works
so up til here I am good. It is this next part that I can't seam to get.
Write a routine which uses Euler's method to solve the equation of motion numerically for velocity v(t):
Test the program by trying a plane with intitial velocity [v0,0] such that it maintains this speed when the engines power is P=P0
We have been given an Esolve we can use:
Esolve:=proc(f::procedure,h,x0,y0,N::integer) # Calculates y(x0+n*h) for n=1..N given y0=y(x0) and f(x,y)
y:=y0; # Start Value
for n from 1 to N do
y[n]:= y[n-1]+h*f(y[n-1],x); # Euler's formula
x:=x+h; # Next x
If anyone could help me understand how it works and how to get this to work with vectors I would be very gratefull.