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  • A global view of the isochronous trajectory families by Hamilton's hodographic transformation

    Paper ID



    • Fang-Toh Sun


    National Tsing Hua University






    An overall view of the characteristic features of the isochronous trajectory families is presented. The trajectories are assumed Keplerian, isoenergetic, and satisfying Lambert's conditions, that is the sum of radial distances of the two termini, and their linear separation are both constant. A geometric approach is adopted by using Hamilton's hodographic transformation. The connection between Hamilton's hodographic isochronism and the Lambert's theorem is briefly reviewed, and the inter-relations among the Hamiltonian set of parameters and the Lambertian sets are developed. The totality of the isochronous trajectory families is then viewed in the velocity space. Various Lambertian invariants as well as some essential non-invariants are examined, and relevant formulas derived. The salient features of some particular isochronous families are then summarized; and Hamilton's time integral is briefly treated. The analysis is essentially 2-dimensional, with its extension to the 3-dimensional case finally discussed.