Hi there,
I'm Tom van Woudenberg, lecturer at Delft University of Technology and I'm
new to this group. I've got the following problem when trying to solve an
ODE with a duhamel integral:
import sympy as sp
omega_n, F_0, m, Omega, zeta = sp.symbols('omega_n, F_0, m, Omega,
zeta',real=True,positive=True)
t = sp.symbols('t',real=True)
u_0, v_0 = sp.symbols('u_0, v_0',real=True)
omega_1, t_tilda = sp.symbols('omega_1, t_tilda',real=True,positive=True)
u_forced = sp.simplify(F_0/m/omega_1
*sp.integrate(sp.sin(Omega*t_tilda)*sp.exp(-zeta*omega_n*(t-t_tilda))*sp.sin(omega_1*(t-t_tilda)),(t_tilda,0,t)))
print(u_forced)
u_forced takes extremely long (I never got a solution) to find on the first
run of the cell in a Jupyter Notebook. If it aborted and I run it another
time, it's found in a couple of seconds:
F_0*(Omega**3*sin(omega_1*t) -
Omega**2*omega_1*exp(omega_n*t*zeta)*sin(Omega*t) -
Omega*omega_1**2*sin(omega_1*t) -
2*Omega*omega_1*omega_n*zeta*exp(omega_n*t*zeta)*cos(Omega*t) +
2*Omega*omega_1*omega_n*zeta*cos(omega_1*t) +
Omega*omega_n**2*zeta**2*sin(omega_1*t) +
omega_1**3*exp(omega_n*t*zeta)*sin(Omega*t) +
omega_1*omega_n**2*zeta**2*exp(omega_n*t*zeta)*sin(Omega*t))*exp(-omega_n*t*zeta)/(m*omega_1*(Omega**4
- 2*Omega**2*omega_1**2 + 2*Omega**2*omega_n**2*zeta**2 + omega_1**4 +
2*omega_1**2*omega_n**2*zeta**2 + omega_n**4*zeta**4))
The same happens in Spyder.
Any ideas of what is causing this issue?
Kind regards,
Tom van Woudenberg
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