• Govindan Rangarajan

      Articles written in Pramana – Journal of Physics

    • Symplectic integration of nonlinear Hamiltonian systems

      Govindan Rangarajan

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      There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called ‘symplectic condition’ (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

    • Spherical aberration and its correction using Lie algebraic methods

      Govindan Rangarajan Minita Sachidanand

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      We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat’s principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

    • Invariant metric for nonlinear symplectic maps

      Govindan Rangarajan Minita Sachidanand

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      In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.

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