oops..i forgot to add a point..the hill curve in the third curve is for cj=3.02 ..the max that is reached in the integration...the initial conditions actually corresspond to a cj=2.9998
hi heimdall, as u rightly pointed out, symplecting algorithms respect the 'invariants' in the problem.
following the std RG methods will give you reasonable results unless u want to integrate for very long periods .
there are many symplecting integration toolboxes available for matlab.
one of...
An additional reference
hi,
the follwoing is a paper that analyses the possiblity of interaction between two Jupiter like planets much after the 'formation' process is over..
shows that one could get ejected with the other orbiting the central star at very small radii...
this is suspected to...