How can I compute Line Integral problem in MATLAB?

Assume the situation where a particle having specific Force Field(vector) moves over a certain curve and you will need to calculate total energy along with the path. This is called as the Line Integral that appears in the area of Mechanics Problem in Physics. Below is the typical equation you may focus:

∫​F⋅dr = ∫F(r(t))⋅r′(t)dt

As far as I looked for, there is no equivalent MATLAB functions or workflow demonstrated in existing documents to solve this sort but could you suggest example solutions for this?

Answer 1

[MathWorks Support Team]

As you mention, there is no explicitly corresponding functions in MATLAB. However, hope following example program helps solve your own Line Integral problem.

Assume that there is a particle having below Force Field and the particle moves anti-clockwise along with the below circle.

r(t) ​= [cos(t)+2;sin(t)​]​  % curve

F(x,y)​ = [−y;x​] % force field

MATLAB program:

syms F1(x,y) F2(x,y) r1(t) r2(t)
r1(t) = cos(t)+2;
r2(t) = sin(t);
F1(x,y) = -y;
F2(x,y) = x;
r = [r1;r2];
F = [F1;F2];
Fr = F(r1(t),r2(t));
dr = diff(r(t),t);
integrand = dot(Fr,dr);
work = int(integrand,t,[0,2*pi])