<s>
Variational	B-Algorithm
integrators	I-Algorithm
are	O
numerical	B-Algorithm
integrators	I-Algorithm
for	O
Hamiltonian	O
systems	O
derived	O
from	O
the	O
Euler	O
–	O
Lagrange	O
equations	O
of	O
a	O
discretized	O
Hamilton	O
's	O
principle	O
.	O
</s>
<s>
Variational	B-Algorithm
integrators	I-Algorithm
are	O
momentum-preserving	O
and	O
symplectic	B-Algorithm
.	O
</s>
<s>
To	O
construct	O
a	O
variational	B-Algorithm
integrator	I-Algorithm
for	O
this	O
system	O
,	O
we	O
begin	O
by	O
forming	O
the	O
discrete	O
Lagrangian	O
.	O
</s>
<s>
Different	O
choices	O
for	O
the	O
approximation	O
to	O
the	O
trajectory	O
and	O
the	O
time	O
integral	O
give	O
different	O
variational	B-Algorithm
integrators	I-Algorithm
.	O
</s>
