I want to solve the below mentioned system of ODEs. However I get the warning "Explicit solution could not be found. > In dsolve at 194 " Can anyone explain me why?

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Prayash
Prayash 2014-11-3
评论： Torsten 2014-11-4
syms v(t)
syms p(t)
syms k
syms g
syms m
o1='Dv= -k*v(t)*v(t)/m - g*sin(p(t))’;
o2='Dp= -g*cos(p(t))/v(t)’;
int=’v(0)=50, p(0)=35’;
[v,p]=dsolve(o1,o2,int)

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回答（2 个）

Zoltán Csáti
Zoltán Csáti 2014-11-3
First of all, the first five lines are not needed. To answer your problem: this nonlinear differential equation system can not be solved by the Symbolic Math Toolbox. I tried to solve it with the more advanced Maple 16, but it couldn't solve either. I suggest you to solve it numerically, or using an approximate analytic method.
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Prayash
Prayash 2014-11-4
编辑：Prayash 2014-11-4
I generated an array of v and p by solving the system of equations numerically and used the below mentioned relations to generate x and y vector and plot the base ball trajectory.
dx/dt=v*cos(p) dy/dt=v*sin(p)
I have been successful in doing so. But how do I obtain the functions v and p by using a numerical approach?

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MA
MA 2014-11-3
you can't solve it unless you have k,g,m parameters
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Torsten
Torsten 2014-11-4
You don't need an explicit function for p and v. If you have p and v in an array at times t(1),...,t(n), just use MATLAB interp1 to interpolate the values for t and p at times in between the t(i)'s.
For an example, take a look at example 3 under
http://www.mathworks.de/help/matlab/ref/ode45.html
Best wishes
Torsten.
Torsten
Torsten 2014-11-4
Or even simpler:
Solve for p,v,x and y simultaneously using ODE45:
dv/dt= -k*v*v/m - g*sin(p)
dp/dt= -g*cos(p)/v
dx/dt = v*cos(p)
dy/dt = v*sin(p)
Best wishes
Torsten.

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