Editing A Symplectic Integrator
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== Introduction == | == Introduction == | ||
− | On | + | On Orbiter Forum, orbinaut Keithth G has described some of his results comparing the Orbiter numerical integrator with one of his own. In response to a user question, he provided the following description of the principles underlying a symplectic numeric integrator. |
== A second-order symplectic integrator == | == A second-order symplectic integrator == | ||
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And that's about all there is to this this second-order symplectic integrator. To integrate, one chooses a suitable small step-size (so that the overall errors are as small as some tolerance that you require for your calculations); one specifies the initial conditions of the object - its position and velocity - and then one repeatedly applies the integration step for as long as you wish. | And that's about all there is to this this second-order symplectic integrator. To integrate, one chooses a suitable small step-size (so that the overall errors are as small as some tolerance that you require for your calculations); one specifies the initial conditions of the object - its position and velocity - and then one repeatedly applies the integration step for as long as you wish. | ||
− | Now, for those interested, it is worthwhile setting up this integrator in, say, | + | Now, for those interested, it is worthwhile setting up this integrator in, say, an spreadsheet and seeing how it performs under various sizes of time-steps. and initial conditions. Of course, if there is more than one gravitating body, then you have additional terms in the force functions, but the basic scheme of the updating rule remains the same. |
As a sequel to this post, I will sketch how you can quickly build fourth and sixth order symplectic integrators from this simple second-order integrator. | As a sequel to this post, I will sketch how you can quickly build fourth and sixth order symplectic integrators from this simple second-order integrator. |