HCRP project 2009
Caustic on graph of quartic parabola
Caustic of parabola
Office: SciCtr 434
Email: knill@math.harvard.edu
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| Geodesics on the paraboloid. This was a test picture after replacing the canned DSolve routines with own Runge Kutta routines which is necessary when doing the evolution on manifolds with different charts and also allows a bit more control in general like assuring that the flow stays on the unit tangent bundle. The surface is the elliptic paraboloid z=x2 + 2 y2. |
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| Same picture but with wave fronts added. |
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| Geodesics and wave fronts on the monkey saddle surface z = 6 x y2-2x3-3y4. |