9. Lie Groups And Rigid-Body Mechanics

2018 ◽  
pp. 243-270
Keyword(s):  
Rigid Body ◽  
Lie Groups ◽  
Rigid Body Mechanics

TWO PROBLEMS OF RIGID BODY MECHANICS

2016 ◽  
Vol 47 (7) ◽  
pp. 775-782
Author(s):  
Vladimir Alekseevich Shvilkin
Keyword(s):  
Rigid Body ◽  
Rigid Body Mechanics

Sir Robert Stawell Ball and methodologies of modern screw theory

2002 ◽  
Vol 216 (1) ◽  
pp. 1-11 ◽  
Author(s):  
H Lipkin ◽  
J Duffy
Keyword(s):  
Computational Geometry ◽  
Rigid Body ◽  
Lie Algebra ◽  
Screw Theory ◽  
Mechanical Design ◽  
Ball Screw ◽  
Dual Numbers ◽  
Body Dynamics ◽  
Rigid Body Mechanics ◽  
Multi Body

The theory of screws was largely developed by Sir Robert Stawell Ball over 100 years ago to investigate general problems in rigid body mechanics. Nowadays, screw theory is applied in many different but related forms including dual numbers, Plilcker coordinates and Lie algebra. An overview of these methodologies is presented along with a perspective on Ball. Screw theory has re-emerged after a hiatus to become an important tool in robot mechanics, mechanical design, computational geometry and multi-body dynamics.

Bézier Curves on Riemannian Manifolds and Lie Groups With Kinematics Applications

1994 ◽  
Author(s):  
Frank C. Park ◽  
Bahram Ravani
Keyword(s):  
Riemannian Manifold ◽  
Rigid Body ◽  
Lie Groups ◽  
Riemannian Manifolds ◽  
Group Structure ◽  
Recursive Algorithm ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Spatial Displacements ◽  
Natural Way

Abstract In this article we generalize the concept of Bézier curves to curved spaces, and illustrate this generalization with an application in kinematics. We show how De Casteljau’s algorithm for constructing Bézier curves can be extended in a natural way to Riemannian manifolds. We then consider a special class of Riemannian manifold, the Lie groups. Because of their algebraic group structure Lie groups admit an elegant, efficient recursive algorithm for constructing Bézier curves. Spatial displacements of a rigid body also form a Lie group, and can therefore be interpolated (in the Bezier sense) using this recursive algorithm. We apply this algorithm to the kinematic problem of trajectory generation or motion interpolation for a moving rigid body.

scholarly journals The Effectivenes of Modeling Instruction Learning on Students’ Conceptual Understanding of Rotational Dynamic

2020 ◽  
Vol 10 (2) ◽  
pp. 158
Author(s):  
Sherly Verlinda ◽  
Sutopo Sutopo ◽  
Eny Latifah
Keyword(s):  
Rigid Body ◽  
Conceptual Understanding ◽  
Mixed Method ◽  
Cognitive Model ◽  
Constructivist Theory ◽  
Develop Model ◽  
Modeling Instruction ◽  
The Subject ◽  
Rigid Body Mechanics ◽  
Multiple Choice Items

Rotational Dynamics is one of the physics topics which is quite difficult for students. Several previous studies showed students’ difficulties on this topic, one of which is the aspect of students’ conceptual understanding. Modeling instruction is the effective approach to improve students’ understanding. This model is in line with constructivist theory and cognitive model theory. This research aimed to examine the effectiveness of modeling instruction that we developed to improve students' conceptual understanding of rigid body mechanics, where the knowledge of particle mechanics serve as anchor or bridging to develop model of rigid body. This research used mixed method with embedded experimental design. It used one group pretest-posttest design and involved 65 students of a high school in Malang as the subject. Data were gathered using test consisting of 17 multiple-choice items with explanation. The students’ scores were analyzed quantitatively using t-test and N-gain to measure the improvement of students’ understanding, while the students' reasons were analyzed qualitatively. The results showed the average students’ score increased from 1.62 to 9.92 with N-gain of 0.54 (in upper medium category). We concluded that the modeling instruction was effective to improve students’ conceptual understanding.

Sign in / Sign up

Export Citation Format

Share Document