Dynamic Analysis of Tippe Top on Cylinder’s Inner Surface With and Without Friction based on Routh Reduction

Abstract

Physics computing can be used to help to solve complex dynamic equations, both translation and rotation. The purpose of this study was to obtain differences in the dynamics of the tippe top with and without friction moving on inner surface of a cylindrical with varying initial state based of Routhian Reduction. The equation of tippe top in flat fields with and without friction has been reduced by the Routhian reduction method with the Poincare equation with computational in the previous research, and computation has also been carried out in the search for numerical solutions to the dynamics of tippe top with friction in the Maple program. In this study the reduction used is a Routhian reduction, so that the equation used in determining the equations of tippe top motion with and without friction that moves in a curved plane in the form of a cylindrical surface with varying initial state based on maple is Poincaré’s equation based on Routhian reduction with and without friction. The effect of friction can be seen clearly through the dynamics and graph equations in the return top. This method can reduce the equation of backward motion with and without friction that moves on the surface of the cylinder clearly in the form of a set of differential equations. This research can be continued by solving the dynamic equations of the tippe top in other curved fields such as the torus and ball. The findings of this study are dynamic equations and graphs of friction with and without friction equations that move in curved fields in the inner of surfaces in cylinders with varying initial state based on maple.

Pemodelan Dinamika Tippe Top (Tt) Dengan Kendala Non-Holonomik Berbasis Komputasi Fisika Pada Bidang Datar (R^2×so(3))

“…Banyak ide dan perkembangan dalam mekanika geometri telah berperan dalam disiplin ilmu lain untuk menangani masalah praktis [1]. Mekanika geometris terapan dapat ditemukan di berbagai bidang seperti robotika, dinamika kendaraan, dan gerak lokomotif pada berbagai gerak hewan yang melibatkan mekanika non-holonomik [2].…”

“…Namun, penelitian mereka tidak menganalisis solusi numerik untuk benda asimetris dengan kendala holonomik. Sistem non-holonomik diperkenalkan dalam mekanika oleh Ariska M, Akhsan H dan Muslim M (2020a), Lewis AD (2017), Ariska M, Akhsan H dan Muslim M (2020b) [2,13,15], yang berarti bahwa sistem mengalami kendala yang membatasi kecepatan partikel sistem dalam ruang konfigurasi [16]. Kendala adalah kondisi yang membatasi gerak suatu sistem mekanis sehingga mengurangi derajat kebebasan [17].…”

“…Metode ini memiliki dua sifat yang diinginkan: penerapan adaptasi langkah waktu yang mudah dan kelonggaran sistem yang mungkin kaku. Untuk sebagian besar proses, kami menggunakan toleransi kesalahan relatif 10 -9 [2,15,17,19]. Perhitungan yang digunakan adalah Maple 18.…”

Routh reducibility and controllability of unstable mechanical systems

“…To this day, the Routh reduction is still part of active research. For example, a new application of the Routh reducibility is presented in [20] and novel examples are revisited such as the tipple top on a cylinder's surface [1]. The Routhian approach served as basis for several generalizations like the new model reduction techniques in [19], or for the extension of the theory like the one for discrete systems in [13].…”

Analysis of college students misconceptions in astronomy using four-tier test

“…Based on the material studied, physics is divided into three states, namely micro physics, visual physics and universe physics. One of the three states of physics is the physics of the universe, which is a physical science that studies the earth and space whose size is so large that it cannot be seen clearly with the naked eye [8]. One of the topics in the physics of the universe is Astronomy.…”