How do I limit angle values in my equations to between 0-90°?

Hi there,

I'm including a simplified version of my code, along with the graph I'm getting from it. What I'm trying to do is to limit the angle m (or m_) to between 0 and 90 degrees only. Can anyone help?

clc

t=[0:0.01:1];
for j=1 : 101
    syms m
    m_ = solve(sind(m)==t(j), m);
    y = zeros(numel(t), numel(m_)); % pre-allocation
    y(j, :)=m_*30+5;
    hold on
    plot (t, y)
end

Answer 1

[Alan Stevens]

This does it

t=[0:0.01:1];
for j=1 : 101
    
    m_ = rad2deg(asin(t(j)));
    y = zeros(numel(t), numel(m_)); % pre-allocation
    y(j, :)=m_*30+5;
    hold on
    plot (t, y)
end

Answer 2

[Jack Cross]

Hi Alan,

I see you solved the equation for m. That's great, the equation I need solving is a bit more complicated for t (see below). It was a bad example as it was easy to solve.

sqrt((2*dl*sind(theta(j)))/(Fy + (T1*dt/(m*dl)+T2*sind(theta(j))/m+W*dc/(m*dl))*cosd(theta(j))*sind(90-theta(j))))=t(j)

Does "rad2deg" help to keep the angles 0-90? Are you able to show a code with that and still keep the solve line in?

[Alan Stevens]

rad2deg doesn't necessarily keep the angles between 0 and 90. but asin(x) where x is anything from 0 to 1, does (well, it keeps it between 0 and pi/2).

If you supply the other variable values, range of t etc. I'll have a look at your more complicated expression.

[Jack Cross]

That makes sence. I just posted the full code. Appreciate your help.

Answer 3

[Jack Cross]

Here's the whole code incase I'm being confusing:

clear all
clc

L=0.01;
g=9.81;
m=0.85;
T1=(L+0.5)*m*g;
T2=(L+0.5)*m*g;
W=m*g;
dc=0.15;
dt=0.3;
dl=0.3;
Fy=L*g;

t=[0:0.25:2.5];
for j=1 : 11
    syms theta
    theta_ = solve(sqrt((2*dl*sind(theta))/(Fy + (T1*dt/(m*dl)+T2*sind(theta)/m+W*dc/(m*dl))*cosd(theta)*sind(90-theta)))==t(j), theta);
    y = zeros(numel(t),numel(theta_)); % pre-allocation
    y(j, :)= dl*sind(theta_);
    hold on
    plot (t, y)
end

[Alan Stevens]

This is the best I can do. I seem to be limited to values of t between 0.1 and 2.47. But all the thetas are less than 90.

dl = 0.3;
t= 0.1:0.01:2.47;
theta_ = zeros(numel(t),1);
for j=1 : numel(t)
    theta0 = 90;
    theta_(j) = fzero(@zerofn,theta0,[],t(j));
end
y= dl*sind(theta_);
hold on
plot (t, y),grid

function F = zerofn(theta,t)
            L=0.01;
            g=9.81;
            m=0.85;
            T1=(L+0.5)*m*g;
            T2=(L+0.5)*m*g;
            W=m*g;
            dc=0.15;
            dt=0.3;
            dl=0.3;
            Fy=L*g;
            
            F = sqrt((2*dl*sind(theta)) ...
                /(Fy + (T1*dt/(m*dl)+T2*sind(theta)/m+W*dc/(m*dl)) ...
                *cosd(theta)*sind(90-theta)))-t;
end

The above produces the following graph:

[Alan Stevens]

By playing around with initial guess theta0 you might be able to get solutions for values of t<0.1 I didn't do that.

[Jack Cross]

Wow, Alan, that looks like a s**t ton of work, thank you so much!

I haven't got time to pick it apart right now, but will look in more detail shortly. The graph looks bang on!

Also, I think I may need to reference you in my dissertation, I will check with my study coach.

[Alan Stevens]

After playing around a bit I managed to fill in the lower end, down to t = 0.01, as follows:

dl = 0.3;
t= 0.01:0.01:2.47;
theta_ = zeros(numel(t),1);
for j=1 : numel(t)
    if t(j)<0.05
        theta0 = 1;
    elseif t(j)<0.1
        theta0 = 8;
    else
        theta0 = 90;
    end
    theta_(j) = fzero(@zerofn,theta0,[],t(j));
end
y= dl*sind(theta_);
hold on
plot (t, y),grid
xlabel('t'),ylabel('y')

function F = zerofn(theta,t)
            L=0.01;
            g=9.81;
            m=0.85;
            T1=(L+0.5)*m*g;
            T2=(L+0.5)*m*g;
            W=m*g;
            dc=0.15;
            dt=0.3;
            dl=0.3;
            Fy=L*g;
            
            F = sqrt((2*dl*sind(theta)) ...
                /(Fy + (T1*dt/(m*dl)+T2*sind(theta)/m+W*dc/(m*dl)) ...
                *cosd(theta)*sind(90-theta)))-t;
end

The resulting graph now looks like:

[Jack Cross]

I'm wondering if at t=0, all forces are in static equilibrium and that's why we're not getting any change in y until after t=0?