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/48
Higher order symplectic
2nd order Velocity Verlet
\(\left\{\begin{array}{ll}v^{k+1/2}&=v^k+\frac{h}{2}\,F(p^k,v^k,t^k)/m \\ p^{k+1}&=p^k+h\,v^{k+1/2} \\ v^{k+1}&=v^{k+1/2}+\frac{h}{2}\,F(p^{k+1},v^{k+1/2},t^{k+1})/m\end{array}\right.\)
- Remains stable with permanent oscillation for \(h\leq \frac{2}{\sqrt{K/m}}\)
- Still simple to implement
Example for 1D elastic spring
for
(
int
k
=
0
;
k
<
N
;
++
k
)
{
v
=
v
+
h
/
2
*
(
-
K
/
m
*
p
);
p
=
p
+
h
*
v
;
v
=
v
+
h
/
2
*
(
-
K
/
m
*
p
);
}