DINAMIKA SISTEM MEKANIK DENGAN KENDALA TAK HOLONOMIK PADA RUANG KONFIGURASI R2 ×T 2 DAN e2 ×T 2; THE DYNAMICS OF MECHANICAL SYSTEM WITH NONHOLONOMIC CONSTRAINTS ON R2 ×T 2 AND e2 ×T 2 CONFIGURATION SPACE

ERNIDAWATI, Muhammad

2011 | Disertasi | PROGRAM STUDI S2 ILMU FISIKA

Tricycle is a simple example of locomotion systems with nonholonomic constraints. Nonholonomic constraints involve velocities of the system and restrict the motion of the system in the phase space. A mechanical system is described by a Riemannan manifold and suitable mathematical objects “living” there. The dynamic of tricycle played on the plane as well as on oblate spheroidal surface has been formulated by making use of the so-called Port Controlled Hamiltonian System (PCHS) method. Unfortunately, this method still leaves undetermined Lagrangian multipliers. It is also difficult to determine the basis that vanishing constraint one-form and diagonalizing the inertia metric. The dynamic is then formulated by making use of another method which is more systematic, that is so-called constrained Levi-Civita connection. The method describes system subjected to nonholonomic constraints and external forces, so the Lagrangian multipliers can be eliminated from the equations

Kata Kunci : dinamika gerak, sistem mekanik, tricycle, kendala tak holonomik, keragaman.