Murilo G. Coutinho

Dynamic Simulations of Multibody Systems

• Gebundenes Buch

Produktbeschreibung

This book is a comprehensive introduction to the techniques needed to produce realistic simulations and animations of particle and rigid body systems. It focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic simulation engines that can be used to generate convincing animations of physical events involving particles and rigid bodies, such as a jet flow of water pushing dry flowers away on a patio. It can also be used to produce accurate simulations of mechanical systems, such as a robotic parts feeder where parts are dropped on a conveyer belt and are positioned and aligned as they hit fences strategically placed on the conveyer and used to align the parts to a specific orientation. The book was written for computer graphics, computer animation, computer-aided mechanical design, and modeling software developers who want to learn and incorporate physically based dynamic simulation features in their own systems. All mathematical algorithms and implementations are described in detail in the appendices.

Produktdetails

• Verlag: Springer, Berlin
• 2001
• Seitenzahl: 379
• Englisch
• Abmessung: 235mm
• Gewicht: 690g
• ISBN-13: 9780387951928
• ISBN-10: 038795192X
• Artikelnr.: 10051393

Inhaltsangabe

Computational dynamics.- Hierarchical representation of 3D polyhedra.- Particle systems.- Rigid body systems.- Articulated rigid body systems.- Appendices: Useful 3D geometrical constructions. Numerical solution of ordinary differential equations of motion. Quaternions. Rigid body mass properties. Useful time derivatives. Convex decomposition of 3D polyhedra. Linear complementarity problem. Software implementation.

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1 Computational Dynamics.- 2 Hierarchical Representation of 3D Polyhedra.- 3 Particle Systems.- 4 Rigid-Body Systems.- 5 Articulated Rigid-Body Systems.- A Useful 3D Geometric Constructions.- A.1 Introduction.- A.2 Projection of a Point on a Line.- A.3 Projection of a Point on a Plane.- A.4 Intersection of a Line Segment and a Plane.- A.5 Closest Point between a Line and a Line Segment.- A.6 Computing the Collision- or Contact-Local Frame from the Collision- or Contact-Normal Vector.- A.7 Representing Cross-Products as Matrix-Vector multiplication.- A.8 Suggested Readings.- B Numerical Solution of Ordinary Differential Equations of Motion.- B.1 Introduction.- B.2 Euler Method.- B.2.1 Explicit Euler.- B.2.2 Implicit Euler.- B.3 Runge-Kutta Method.- B.3.1 Second-Order Runge-Kutta Method.- B.3.2 Forth-Order Runge-Kutta Method.- B.4 Using Adaptive Time-Step Sizes to Speed Computations.- B.5 Suggested Readings.- C Quaternions.- C.1 Introduction.- C.2 Basic Quaternion Operations.- C.2.1 Addition.- C.2.2 Dot product.- C.2.3 Multiplication.- C.2.4 Conjugate.- C.2.5 Module.- C.2.6 Inverse.- C.3 Unit Quaternions.- C.4 Rotation-Matrix Representation Using Unit Quaternions.- C.5 Advantages of Using Unit Quaternions.- C.6 Suggested Readings.- D Rigid-Body Mass Properties.- D.1 Introduction.- D.2 Mirtich's Algorithm.- D.2.1 Volume-Integral to Surface-Integral Reduction..- D.2.2 Surface-Integral to Projected-Surface-Integral Reduction.- D.2.3 Projected-Surface-Integral to Line-Integral Reduction.- D.2.4 Computing the Line Integrals from the Vertex Coordinates.- D.3 Suggested Readings.- E Useful Time Derivatives.- E.1 Introduction.- E.2 Computing the Time Derivative of a Vector Attached to a Rigid Body.- E.3 Computing the Time Derivative of a Contact-Normal Vector.- E.3.1Particle-Particle Contact.- E.3.2 Rigid Body-Rigid Body Contact.- E.4 Computing the Time Derivative of the Tangent Plane.- E.5 Computing the Time Derivative of a Rotation Matrix.- E.6 Computing the Time Derivative of a Unit Quaternion.- E.7 Suggested Readings.- F Convex Decomposition of 3D Polyhedra.- F.1 Introduction.- F.2 Joe's Algorithm.- F.2.1 Determining Candidate Cut Planes.- F.2.2 Computing the Cut Face Associated with a Cut Plane.- F.2.3 Termination Conditions.- F.3 Suggested Readings.- G The Linear-Complementarity Problem.- G.1 Introduction.- G.2 Dantzig's Algorithm: The Frictionless Case.- G.2.1 Termination Conditions.- G.3 Baraff's Algorithm: Coping with Friction.- G.3.1 Static-Friction Conditions.- G.3.2 Dynamic Friction.- G.3.3 Termination Conditions.- G.4 Suggested Readings.- H Software Implementation.- References.

Rezensionen

From the reviews:

"This is a monograph intended to provide its readers with a comprehensive introduction to the simulation and animation of multibody system dynamics. Both theoretical and applied concepts are discussed. The book is written for the designers of software to represent the kinematics and dynamics of systems of rigid bodies. ... The book contains a vast store of information on computer graphics and the associated procedures." (Ronald L. Huston, Zentralblatt MATH, Vol. 976, 2002)