问题描述
我目前正在求解非线性 ODE 系统.这是一组运动学运动方程,我需要在其中计算给定角速度的位置角
I am currently solving a system of nonlinear ODE's. It is a set of kinematic motion equations, where I need to calculate the position angles with given anguar velocities
我发现如何使用列表添加依赖于时间的函数,但问题是,如何添加一个也依赖于时间但作为向量给出的参数.
I found out, how to add a function dependent on time using the list, but the question is, how to add a parameter which is also time dependent, but given as a vector.
简化是用下面的代码写的.c(t) 是一个时间函数.
Simplified is it written in the following code. c(t) is a time function.
function dx = f(t, x, c)
dx(1) = x(1)*sin(x(2))
dx(2) = c*x(2)*cos(x(1))
dx(3) = t*cos(x(3))
endfunction
c = 1:32; // values from measured signal, here simplyfied
y0 = [0.1;0.1;0.1];
t0 = 0;
t = 0:0.1:%pi;
y = ode(y0, t0, t, list (f, c));
推荐答案
见
- https://help.scilab.org/doc/5.5.2/en_US/interp1.html 和
- https://help.scilab.org/doc/5.5.2/en_US/interpln.html
关于如何将函数表转换为插值函数.
on how to convert a function table into an interpolating function.
本质上,在右侧函数 dx=f(t,x,tc_arr)
中,您评估
Essentially, in the right side function dx=f(t,x,tc_arr)
you evaluate
function dx=f(t,x,tc_arr)
c = interpln(tc_arr, t)
dx(1) = x(1)*sin(x(2))
dx(2) = c*x(2)*cos(x(1))
dx(3) = t*cos(x(3))
endfunction
其中 tcarr
包含采样时间和采样值的数组.
where tcarr
contains arrays of sampling times and sampling values.
以信号为例
t_sam = -1:0.5:4;
c_sam = sin(2*t_sam+1);
tc_arr = [ t_sam; c_sam ];
请注意,您始终需要采样时间来了解输入时间 t
与值数组的关系.
Note that you always will need the sample times to find out how the input time t
relates to the value array.
t = 1.23;
c = interpln(tc_arr, t)
返回c = - 0.2719243
.
您也可以使用其他函数,它在插值方法方面有更多选择.
You could as well use the other function, which has more options in terms of interpolation method.
function dx=f(t,x,t_sam,c_sam)
c = interp1(t_sam, c_sam, t, "spline", "extrap")
dx(1) = x(1)*sin(x(2))
dx(2) = c*x(2)*cos(x(1))
dx(3) = t*cos(x(3))
endfunction
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