Python - Strange plot points on ode

Question

I'm currently developing a dynamic model for a vehicle as part of my master thesis.

I'm using the ode solver that comes with python, and I get results that seem good. But I notice a problem with some of the plots.

Part of my code is as follows:

 f = [#0 - x_ctr     
            dx_ctrdt,
        #1 - dx_ctrdt
            (flx_car1_A + flx_car1_B + flx_car2_A + flx_car2_B)/M_car + (x_ctr)*(V_tr**2)/R_curve/R_ctr - F_drag/M_car,
        #2 - y_ctr     
            dy_ctrdt,
        #3 - dy_ctrdt
            (fly_car1_A + fly_car1_B + fly_car2_A + fly_car2_B)/ M_car + (R_curve + y_ctr)*(V_tr**2)/R_curve/R_ctr - 9.8*np.sin(beta),
        #4 - omega_1
            -(flx_car1_A + flx_car1_B)*r/Inertia_1 - 0.5*F_rr*r/Inertia_1 + F_motor_1*r/Inertia_1,
        #5 - omega_2
            -(flx_car2_A + flx_car2_B)*r/Inertia_2 - 0.5*F_rr*r/Inertia_2 + F_motor_2*r/Inertia_2,
        #6 - alpha
            dalphadt,  
        #7 - dalphadt
            (mz_car_1  + mz_car_2 ) / Inertia_car,                            
        #8 - x_1A
            v_1A*cos_theta_1 - (V_tr/R_curve)*R_1A*cos_psi_1A,
        #9 - y_1A
            v_1A*sin_theta_1 - (V_tr/R_curve)*R_1A*sin_psi_1A,
        #10 - x_1B
            v_1B*cos_theta_1 - (V_tr/R_curve)*R_1B*cos_psi_1B,
        #11 - y_1B
            v_1B*sin_theta_1 - (V_tr/R_curve)*R_1B*sin_psi_1B,
        #12 - x_2A
            v_2A*cos_theta_2 - (V_tr/R_curve)*R_2A*cos_psi_2A,
        #13 - y_2A
            v_2A*sin_theta_2 - (V_tr/R_curve)*R_2A*sin_psi_2A,
        #14 - x_2B
            v_2B*cos_theta_2 - (V_tr/R_curve)*R_2B*cos_psi_2B,
        #15- y_2B
            v_2B*sin_theta_2 - (V_tr/R_curve)*R_2B*sin_psi_2B,
        ]

When I make a plot of the solutions of f, I get a smooth plot.

dif_var_initial = [0.000, 0.000,    y_ctr_0,  -0.000, 140.0027, 140.0027, 0.000 ,  0.000,  x_1A_0, y_1A_0,  x_1B_0,  y_1B_0,  x_2A_0,  y_2A_0, x_2B_0, y_2B_0]

def dif_eqts(dif_var, t, kx1, ky1, cy1, M_car):
    global v_ax_1, v_ax_2,R_ctr,psi_ctr,Lamb_tk, A_tk, Time_max, delta_t, y_track_1_vector ,y_track_2_vector,R_curve, dRdt,z,j,v_1A,v_1B,v_2A,v_2B,P

    x_ctr, dx_ctrdt, y_ctr, dy_ctrdt, omega_1, omega_2, alpha, dalphadt, x_1A, y_1A, x_1B, y_1B, x_2A, y_2A, x_2B, y_2B = dif_var 

    #   Track disturbances
    eps_ax_1 = A_tk * np.sin(2.*np.pi*(V_tr/Lamb_tk)*t)
    eps_ax_1_tracker.append(eps_ax_1)
    .
    .
    .

But, when I make a graph using for example eps_ax_1_tracker I get strange plots that are not smooth.(The program is obviously more than this but I don't want to bore you with reading many lines of code.)

For exemple:

and closer:

Is this behavior normal? I have searched for similar problems but didn't find anything that could help me.

I hope you have some suggestions why this is happening and thank you so much for your help.

Edit(1)

I get an output for x_ctr as follows: x_ctr

and for forces as: forces

The oscillating behavior is do the irregularities in rail tracks. I hope this helps.

I put two more plots of the outputs, I don't know if you need other type of data. — Nate, Apr 26 '18 at 15:58

score 0 · Accepted Answer · answered Apr 26 '18 at 18:24

Numerical solvers use "probing" values at states that are close but not on the solution trajectory. Loosely speaking, this samples the direction field around the trajectory so that the computed value for the next step may be more accurate. Use the documented paths to obtain the output, in scipy.integrate.ode use the dense output via sol_out or similar, see Using adaptive step sizes with scipy.integrate.ode, for scipy.integrate.odeint use the time list input argument to define the sample points that are reported in the output.

Thank you so much for your answer. I have been exploring a bit and I believe you are right. Now I'm more certain of what is happening. I will implement what you suggested. — Nate, Apr 26 '18 at 18:32

Python - Strange plot points on ode

1 Answers1