For loop help needed

How would I write the following equations in a for loop?

rho = 1.2*exp(h^1.15)
D = .5*rho
Uy=D*cos(theta)
Ux=D*sin(theta)
h_t+dt=h_t+Uy*dt
theta_t+dt=atan(Ux/Uy)

I have an initial value of h=0 and theta=0.

Someone please help. The way I'm thinking about it now creates a circular loop so I don't know what to do.

[Chad Greene]

What's your end goal? What variable are you trying to calculate?

[Shannon Hemp]

I want to find the values of Ux and Uy for time 0 to 10 seconds

[Roger Stafford]

By any chance, are the last two equations supposed to represent the differential equations:

dh/dt = h + Uy
dtheta/dt = atan(Ux/Uy)

If so, you should use, for example, 'ode45' to solve these equations.

The notation you have used is not in accordance with usual mathematical practice. Try expressing your idea in ordinary English rather than mathematical equations to see if you can get your idea across to those of us in this forum.

Answer 1

[John BG]

Correct if wrong but your start equations really are:

rho = 1.2*exp(h^1.15)
D = .5*rho
Uy=D*cos(theta)
Ux=D*sin(theta)
h(t+dt)=h(t)+Uy*dt
theta(t+dt)=atan(Ux/Uy)

Simplifying,

D = .6*exp(h^1.15)  % rid rho
d(h(t))/dt=Uy
d(theta(t))/dt=atan(Ux/Uy)
Ux/Uy=cos(theta)/sin(theta)

because

atan(Ux/Uy)=atan(cos(theta)./sin(theta))=pi/2*sawtooth(2*theta)

testing this:

x = -6*pi:0.01:6*pi
      axis([-6*pi 6*pi -2 2])
      hold all
      plot(x,atan(cos(x)./sin(x)));grid on
      plot(x,pi/2*sawtooth(2*x,0))

then, probably, your start DE system is:

dot_h=U.6*exp(h^1.15)*cos(theta)
dot_theta=pi/2*sawtooth(2*theta)

Over to you, can you solve this? or do you need further help?

If you find this answer of any help solving your question, please click on the thumbs-up vote link,

thanks in advance

John

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