Several tangent vectors on curve

Hello,

I have the following curve plotted:

Now, I want 10 tangent vectors along this curve and I can't seem to figure out how to write the code for this to work. I wrote the following:

t = linspace(-2.5,2.5,100);
x = t.^3 - 4*t;
y = t.^2;
plot(x,y,'LineWidth',2)
axis equal
hold on

i=1:10:100;  
ts=t(i);
xs=x(i); 
ys=y(i); 

tx = ts.^3 -4*ts;
ty = ts.^2;
quiver(tx,ty,xs,ys,'LineWidth',2,'Color','r')
hold off

and the result is.. not quite it:

Any help or advice is appreciated.

Answer 1

[the cyclist]

Well, you never actually calculated the tangent, so it is not that surprising you didn't get the correct result.

t = linspace(-2.5,2.5,100);
x = t.^3 - 4*t;
y = t.^2;

dydt = 2*t;
dxdt = 3*t.^2 - 4;
dydx = dydt./dxdt;

i=1:10:100;  
ts=t(i);
xs=ones(size(i)); 
ys=dydx(i); 

tx = ts.^3 -4*ts;
ty = ts.^2;

figure
hold on
plot(x,y,'LineWidth',2)
quiver(tx,ty,xs,ys,'LineWidth',2,'Color','r')
axis equal

Apologies for rearranging your code to my liking. See this page for the math of calculating the tangent of a parametric equation. (You'll need to be careful if dx/dt is ever zero, because you divide by that.)

Also, I was lazy and just set the length of the x-component of the tangent vector to (positive) 1, then calculated the y-component. You probably want something less lazy.

[Viktor Karlsson]

Thank you so much. I can't really see why the vectors change direction at the bottom though? Should they not continue in the same pattern?

[the cyclist]

As I mentioned, I always defined the x-component of the tangent vector as +1; therefore, it will always be toward the right.

The parametric equation has no inherent "direction", and the tangent line extends in both directions from any given point.

[Viktor Karlsson]

I understand, thank you helping!