求解两个联立的二阶常微分方程 (我的方程) - 未名空间MITBBS历史存档

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求解两个联立的二阶常微分方程 (我的方程)

求解两个联立的二阶常微分方程 (我的方程)# Computation - 科学计算

s*n2003-07-17 07:07

1 楼

我的方程如下：
U=2*Sin(alpha*t)
P=f1(e, de/dt, dphai/dt,theta,U) (关系式已知)
WX=Integrate (P*cos(theta)), theta varies in[0, pi]
WY=Integrate (P*sin(theta)), theta varies in[0, pi]
Fcos(phai)=WX(e,de/dt,dphai/dt)+m*(d2e/d2t)-m*e*(dphai/dt)*(dphai/dt) (1)
Fsin(phai)=WY(e,de/dt,dphai/dt)+m*e*(d2phai/d2t)+2*m*(de/dt)*(dphai/dt) (2)
Objective: Solve (1) and (2) for e(t) and phai(t).
Known: F, m,
Initial conditions: e(0)=0.5, phai(0)=0.5, de and dphai are assumed to be
zero.
My approa

c*e2003-07-17 07:07

2 楼

I have seen a lot of people favoring Runge Kutta method.
In most cases, it is unnecessarily complicated. If you
just want to solve it, convert to 1st order system and use
matlab ode solvers. Much easier and straight forward.
I am not quite sure if your problem can be solved in this way.
I always use matlab as my first approach.

【在 s*********n 的大作中提到】

: 我的方程如下：
: U=2*Sin(alpha*t)
: P=f1(e, de/dt, dphai/dt,theta,U) (关系式已知)
: WX=Integrate (P*cos(theta)), theta varies in[0, pi]
: WY=Integrate (P*sin(theta)), theta varies in[0, pi]
: Fcos(phai)=WX(e,de/dt,dphai/dt)+m*(d2e/d2t)-m*e*(dphai/dt)*(dphai/dt) (1)
: Fsin(phai)=WY(e,de/dt,dphai/dt)+m*e*(d2phai/d2t)+2*m*(de/dt)*(dphai/dt) (2)
: Objective: Solve (1) and (2) for e(t) and phai(t).
: Known: F, m,
: Initial conditions: e(0)=0.5, phai(0)=0.5, de and dphai are assumed to be

s*n2003-07-17 07:07

3 楼

First, thanks for your concerns.
I did try Matlab ode solver. But I was faced with difficuty in time step
control. The ode function needs call another function which is time dependent.
I tried ode solvers several times. It didn't work for me in this case.

【在 c*******e 的大作中提到】

: I have seen a lot of people favoring Runge Kutta method.
: In most cases, it is unnecessarily complicated. If you
: just want to solve it, convert to 1st order system and use
: matlab ode solvers. Much easier and straight forward.
: I am not quite sure if your problem can be solved in this way.
: I always use matlab as my first approach.

s*n2003-07-17 07:07

4 楼

I have solved it. Thanks all. A sign error in the equation that I used to
derive my equations blocked me a couple of months.

dependent.

【在 s*********n 的大作中提到】

: First, thanks for your concerns.
: I did try Matlab ode solver. But I was faced with difficuty in time step
: control. The ode function needs call another function which is time dependent.
: I tried ode solvers several times. It didn't work for me in this case.