DINAMIKA SISTEM MEKANIK TAK HOLONOMIK DENGAN RUANG KONFIGURASI S2 x T3 (SNAKEBOARD; THE DYNAMICS OF A NON HOLONOMIC MECHANICAL SYSTEM WITH CONFIGURATION SPACE S2 x T3 (SNAKEBOARD)

Muharani Asnal, Muhammad Farchani Rosyid

2011 | Disertasi | PROGRAM STUDI S2 ILMU FISIKA

manifold are represented by a set of 1-forms which are non-degenerate. The constraint then induces a distribution of vector fields in which the values of all constraint 1-forms vanish. When the associated distribution is not involutive (or integrabel), then the constraint is said to be nonholonomic. The motion of a snakeboard on a (curved) arena is an instance of a mechanical system with a nonholonomic constraint. We have studied the motion of snakeboard on the internal surface of a sphere in which we assumed that the radius of the spherical arena is so great and the involved energy is small enough so that the motion of the snakeboard is limited around the nadir point of the sphere. We have derived the constraint 1-forms of the system. The dynamical equations of the system were then derived by making use of PCHS the so-called Port-Controlled Hamiltonian System as well as constrained Leci-Civita connection method on the configuration manifold. The PCHS method faced some difficulties concerning the determination of basis vanishing the constraint one-forms and diagonalizing the inertia metric. On the other hand, the constrained Levi-Civita connection method worked systematically resulting in the equation of motion of the snake board on the spherical arena.

Kata Kunci : keragaman, kendala, dinamika, snakeboard