Dynamics of Machines - Part II - IFS.pdf

1.6.5 Comparison between the Analytical and Numerical Solutions of Equation of
Motion
(a) y(t) [m]
0.01
0.005
0
−0.005
(a) Exact Solution − (b) Numerical Solution (delta T = 0.3605 s) − (c) Comparison
−0.01
0 1 2 3 4 5
time [s]
6 7 8 9 10
0.4
(b) y(t) [m]
(c) y(t) [m]
0.2
0
−0.2
−0.4
0 1 2 3 4 5
time [s]
6 7 8 9 10
0.4
0.2
0
−0.2
−0.4
0 1 2 3 4 5
time [s]
6 7 8 9 10
Figure 5: Comparison between the analytical and numerical solutions when a time step of
0.3605 [s] is used – Divergence and numerical instability.
(a) y(t) [m]
(b) y(t) [m]
(c) y(t) [m]
0.01
0.005
0
−0.005
(a) Exact Solution − (b) Numerical Solution (delta T = 0.3 s) − (c) Comparison
−0.01
0 1 2 3 4 5
time [s]
6 7 8 9 10
0.02
0.01
0
−0.01
−0.02
0 1 2 3 4 5
time [s]
6 7 8 9 10
0.02
0.01
0
−0.01
−0.02
0 1 2 3 4 5
time [s]
6 7 8 9 10
Figure 6: Comparison between the analytical and numerical solutions when a time step of 0.3 [s]
is used – Divergence between the numerical and analytical solution due to a roof time step.
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