How to integrate linear system of vectorial equations?

2 次查看（过去 30 天）
Anshuman Pal
Anshuman Pal 2021-8-20
评论： Star Strider 2021-8-22
Hello,
I have the following system of vectorial equations that describe a curve in space r, its tangent vector t and its normal $n$, parametrised by the arc length s:
Suppose I have the function given as a vector of values, as well as initial values of r, t and n. Then is there some simple way (or package) for numerically integrating this system of vectorial equations?
Thank you very much!

请先登录，再回答此问题。

采纳的回答

Star Strider
Star Strider 2021-8-20
Ran in:
syms kappa n(s) r(s) s t(s) r0 t0 n0 Y
Eqn = [diff(r) == t; diff(t) == -r + kappa*n; diff(n) == -kappa*t];
rtn = dsolve(Eqn, r(0)==r0, t(0)==t0, n(0)==n0)
rtn = struct with fields:
t: [1×1 sym] r: [1×1 sym] n: [1×1 sym]
t = simplify(rtn.t, 500)
t = 
r = simplify(rtn.r, 500)
r = 
n = simplify(rtn.n, 500)
n = 
Alternatively:
[VF,Subs] = odeToVectorField(Eqn)
VF = 
Subs = 
rtnfcn = matlabFunction(VF, 'Vars',{s,Y,kappa})
rtnfcn = function_handle with value:
@(s,Y,kappa)[kappa.*Y(3)-Y(2);Y(1);-kappa.*Y(1)]
Use ‘rtnfcn’ with the approopriate numeric ODE solver (for example 0de45, ode15s) depending on the magnitude of κ.
For example:
sspan = linspace(0,10); % Vector Of 's' Values
initconds = rand(3,1); % Initial Conditions
[s,rtn] = ode15s(@(s,rtn,kappa), sspan, initconds); % Integrate
figure
plot(s, rtn)
grid
.
  4 个评论
显示 2更早的评论
Anshuman Pal
Anshuman Pal 2021-8-22
Thank you! A couple more comments:
1) Is there a typo in `ode15s(@(s,rtn,kappa), sspan, initconds)`? Shouldn't it be `ode15s(@rtnfcn, sspan, initconds)`?
2) Can I use `rtnfcn` with a boundary-value solver like `bvp4c`?
Star Strider
Star Strider 2021-8-22
As always, my pleasure!
‘Is there a typo in `ode15s(@(s,rtn,kappa), sspan, initconds)`? ’
There is. It should be:
[s,rtn] = ode15s(@(s,rtn) rtnfcn(s,rtn,kappa), sspan, initconds); % Integrate
‘Can I use `rtnfcn` with a boundary-value solver like `bvp4c`?’
Probably. One addition would be to create ‘kappa’ as an anonymous function, for example with ‘s’ as the independent variable and ‘kapa’ as the dependent variable:
kapamtx = [s(:) kapa(:)];
kappa = @(s) interp1(kapamtx(:,1), kapamtx(:,2), s);
It would be necessary either to keep ‘s’ within the limits of ‘kapamtx(:,1)’ in order to avoid either extrapolating or returning NaN values for ‘s’ outside that range.
.

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Numerical Integration and Differential Equations 的更多信息

标签

产品


版本

R2020b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by