用龙格库塔方法求解船舶横摇运动微分方程:θ ̈+α_1 θ ̇+α_2 θ ̇|θ ̇ |+α_3 θ ̇^3+C_1 θ-C_2 θ^3=λθ^2 X(t),X(t)为泊松白噪声扰动,α_1=0.1,α_2=0.02,α_3=0.01,C_1 =1,C_2=1,λ=1,步长 0.001,步数5000000,总时间t=5000,初始条件为0.5,要求用vs2013中Fortran语言实现。
时间: 2024-02-13 16:03:26 浏览: 90
以下是Fortran语言实现的代码,使用龙格库塔方法求解船舶横摇运动微分方程:
```fortran
program ship_motion
implicit none
integer, parameter :: dp = selected_real_kind(15, 307)
real(dp) :: alpha1 = 0.1_dp, alpha2 = 0.02_dp, alpha3 = 0.01_dp
real(dp) :: c1 = 1.0_dp, c2 = 1.0_dp, lambda = 1.0_dp
real(dp) :: dt = 0.001_dp, t = 0.0_dp, tmax = 5000.0_dp
real(dp) :: theta, thetadot, thetaddot, x, r1, r2, r3, r4, k1, k2, k3, k4
integer :: i, nsteps = int(tmax/dt)
! Initial conditions
theta = 0.5_dp
thetadot = 0.0_dp
do i = 1, nsteps
! Generate Poisson white noise
x = lambda*dt + sqrt(lambda*dt)*rand()
! Compute coefficients
r1 = alpha1*thetadot
r2 = alpha2*thetadot*abs(thetadot)
r3 = alpha3*thetadot**3
k1 = thetadot
k2 = thetadot + 0.5*dt*(r1 + r2 + r3 + c1*theta - c2*theta**3)
r1 = alpha1*k2
r2 = alpha2*k2*abs(k2)
r3 = alpha3*k2**3
k3 = thetadot + 0.5*dt*(r1 + r2 + r3 + c1*k2 - c2*k2**3)
r1 = alpha1*k3
r2 = alpha2*k3*abs(k3)
r3 = alpha3*k3**3
k4 = thetadot + dt*(r1 + r2 + r3 + c1*k3 - c2*k3**3)
thetaddot = (k1 + 2.0_dp*k2 + 2.0_dp*k3 + k4)/6.0_dp
! Update variables
theta = theta + dt*thetadot
thetadot = thetadot + dt*thetaddot
t = t + dt
! Output results
write(*,*) t, theta, thetadot, x
end do
end program ship_motion
```
其中,rand()函数用于生成0到1之间的随机数,可以使用随机数生成器替代。输出结果包括时间、角度、角速度和白噪声扰动。请注意,本代码仅供参考,可能需要根据具体情况进行修改调整。
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