非线性微分方程的求解方程组-g*sinθ-k*v^2=dv/dt___(1)g*cosθ=v*dθ/dt________(2)初值条件v=v0θ=θ0g和k均为常数解析法或数值法均可,数值解法最好给出matlab或C语言程序
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![非线性微分方程的求解方程组-g*sinθ-k*v^2=dv/dt___(1)g*cosθ=v*dθ/dt________(2)初值条件v=v0θ=θ0g和k均为常数解析法或数值法均可,数值解法最好给出matlab或C语言程序](/uploads/image/z/10429620-60-0.jpg?t=%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E7%9A%84%E6%B1%82%E8%A7%A3%E6%96%B9%E7%A8%8B%E7%BB%84-g%2Asin%CE%B8-k%2Av%5E2%3Ddv%2Fdt___%281%29g%2Acos%CE%B8%3Dv%2Ad%CE%B8%2Fdt________%282%29%E5%88%9D%E5%80%BC%E6%9D%A1%E4%BB%B6v%3Dv0%CE%B8%3D%CE%B80g%E5%92%8Ck%E5%9D%87%E4%B8%BA%E5%B8%B8%E6%95%B0%E8%A7%A3%E6%9E%90%E6%B3%95%E6%88%96%E6%95%B0%E5%80%BC%E6%B3%95%E5%9D%87%E5%8F%AF%2C%E6%95%B0%E5%80%BC%E8%A7%A3%E6%B3%95%E6%9C%80%E5%A5%BD%E7%BB%99%E5%87%BAmatlab%E6%88%96C%E8%AF%AD%E8%A8%80%E7%A8%8B%E5%BA%8F)
非线性微分方程的求解方程组-g*sinθ-k*v^2=dv/dt___(1)g*cosθ=v*dθ/dt________(2)初值条件v=v0θ=θ0g和k均为常数解析法或数值法均可,数值解法最好给出matlab或C语言程序
非线性微分方程的求解
方程组
-g*sinθ-k*v^2=dv/dt___(1)
g*cosθ=v*dθ/dt________(2)
初值条件
v=v0
θ=θ0
g和k均为常数
解析法或数值法均可,数值解法最好给出matlab或C语言程序
非线性微分方程的求解方程组-g*sinθ-k*v^2=dv/dt___(1)g*cosθ=v*dθ/dt________(2)初值条件v=v0θ=θ0g和k均为常数解析法或数值法均可,数值解法最好给出matlab或C语言程序
知道dsolve函数就好求常微分方程或方程组了:)
>> s=dsolve('Dv=-k*v-g*sin(a),Da=g*cos(a)/v','v(0)=v0,a(0)=a0');
>> a=s.a
a =(-g*cos(a0)+a0*v0*k)/v0/k+g*cos(a0)/v0/k*exp(k*t)
>> v=s.v
v =1/cos(a0)*v0/exp(k*t)*cos((-g*cos(a0)+a0*v0*k)/v0/k+g*cos(a0)/v0/k*exp(k*t))
>>
知道dsolve函数就好求常微分方程或方程组了:)
>> s=dsolve('Dv=-k*v-g*sin(a),Da=g*cos(a)/v','v(0)=v0,a(0)=a0');
>> a=s.a
a =(-g*cos(a0)+a0*v0*k)/v0/k+g*cos(a0)/v0/k*exp(k*t)
>> v=s.v
v =1/cos(a0)*...
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知道dsolve函数就好求常微分方程或方程组了:)
>> s=dsolve('Dv=-k*v-g*sin(a),Da=g*cos(a)/v','v(0)=v0,a(0)=a0');
>> a=s.a
a =(-g*cos(a0)+a0*v0*k)/v0/k+g*cos(a0)/v0/k*exp(k*t)
>> v=s.v
v =1/cos(a0)*v0/exp(k*t)*cos((-g*cos(a0)+a0*v0*k)/v0/k+g*cos(a0)/v0/k*exp(k*t))
>>
应该室这样?
收起
把初始值和常数给出,用数值解法。
function hh
[t,y]=ode45(@fun,[1,2],[10 10])
plot(t,y)
function yhat=fun(t,x)
theta=x(1);v=x(2);g=9.8;k=0.022;
yhat=[g*cos(theta)/v;-g*sin(theta)-k*v^2];