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Vector Mechanics for Engineers: Statics and Dynamics

01 Jan 2017-
TL;DR: In this article, the authors present a simulation of the physics of rigid bodies in three dimensions and three dimensions in the plane motion of Rigid Bodies: forces and acceleration, energy and momentum, and moments of inertia.
Abstract: 1 Introduction 2 Statics of Particles 3 Rigid Bodies: Equivalent Systems of Forces 4 Equilibrium of Rigid Bodies 5 Distributed Forces: Centroids and Centers of Gravity 6 Analysis of Structures 7 Forces in Beams and Cables 8 Friction 9 Distributed Forces: Moments of Inertia 10 Method of Virtual Work 11 Kinematics of Particles 12 Kinetics of Particles: Newton's Second Law 13 Kinetics of Particles: Energy and Momentum Methods 14 Systems of Particles 15 Kinematics of Rigid Bodies 16 Plane Motion of Rigid Bodies: Forces and Accelerations 17 Plane Motion of Rigid Bodies: Energy and Momentum Methods 18 Kinetics of Rigid Bodies in Three Dimensions 19 Mechanical Vibrations Appendix Fundamentals of Engineering Examination
Citations
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Proceedings Article•DOI•
24 Jul 1994
TL;DR: This paper offers improved registration in two areas: accurate static registration across a wide variety of viewing angles and positions and dynamic errors that occur when the user moves his head are reduced by predicting future head locations.
Abstract: In Augmented Reality, see-through HMDs superimpose virtual 3D objects on the real world. This technology has the potential to enhance a user's perception and interaction with the real world. However, many Augmented Reality applications will not be accepted until we can accurately register virtual objects with their real counterparts. In previous systems, such registration was achieved only from a limited range of viewpoints, when the user kept his head still. This paper offers improved registration in two areas. First, our system demonstrates accurate static registration across a wide variety of viewing angles and positions. An optoelectronic tracker provides the required range and accuracy. Three calibration steps determine the viewing parameters. Second, dynamic errors that occur when the user moves his head are reduced by predicting future head locations. Inertial sensors mounted on the HMD aid head-motion prediction. Accurate determination of prediction distances requires low-overhead operating systems and eliminating unpredictable sources of latency. On average, prediction with inertial sensors produces errors 2-3 times lower than prediction without inertial sensors and 5-10 times lower than using no prediction at all. Future steps that may further improve registration are outlined.

509 citations

Book•
25 Aug 2008
TL;DR: This book discusses the foundations of Biomechanics and Qualitative Analysis, and its applications in Physical Education, Sports Medicine and Rehabilitation, and Mechanics of the Musculoskeletal System.
Abstract: Preface. Part 1: Introduction. 1. Introduction to the Biomechanics of Human Movement. 2. Fundamentals of Biomechanics and Qualitative Analysis. Part 2: Biological/Structural Bases. 3. Anatomical Description and its Limitations. 4. Mechanics of the Musculoskeletal System. Part 3: Mechanical Bases. 5. Linear and Angular Kinetics. 6. Linear Kinetics. 7. Angular Kinetics. 8. Fluid Mechanics. Part 4: Applications of Biomechanics in Qualitative Analysis. 9. Applying Biomechanics in Physical Education. 10. Applying Biomechanics in Coaching. 11. Applying Biomechanics in Strength and Conditioning. 12. Applying Biomechanics in Sports Medicine and Rehabilitation. References. Appendix A: Glossary. Appendix B: Conversion Factors. Appendix C: Suggested Answers to Selected Review Questions. Appendix D: Right Angle Trigonometry Review. Appendix E: Qualitative Analysis in Biomechanical Principles. Index. Lab Activities. About the Author. Index.

327 citations

Journal Article•DOI•
TL;DR: In this article, a general and comprehensive analysis on the continuous contact force models for soft materials in multibody dynamics is presented throughout this work, and the force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process.
Abstract: A general and comprehensive analysis on the continuous contact force models for soft materials in multibody dynamics is presented throughout this work. The force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. In a simple way, these contact force models are based on the analysis and development of three main issues: (i) the dissipated energy associated with the coefficient of restitution that includes the balance of kinetic energy and the conservation of the linear momentum between the initial and final instant of contact; (ii) the stored elastic energy, representing part of initial kinetic energy, which is evaluated as the work done by the contact force developed during the contact process; (iii) the dissipated energy due to internal damping, which is evaluated by modeling the contact process as a single degree-of- freedom system to obtain a hysteresis damping factor. This factor takes into account the geometrical and material properties, as well as the kinematic characteristics of the contacting bodies. This approach has the great merit that can be used for contact problems involving materials with low or moderate values of coefficient of restitution and, therefore, accommodate high amount of energy dissipation. In addition, the resulting contact force model is suitable to be included into the equations of motion of a multibody system and contributes to their stable numerical resolution. A demonstrative example of application is used to provide the results that support the analysis and discussion of procedures and methodologies described in this work.

314 citations

Journal Article•DOI•
Shaobo Huang1, Ning Fang1•
TL;DR: The research findings from the present study imply that if the goal of the instructor is to predict the average academic performance of his/her dynamics class as a whole, the instructor should choose the simplest mathematical model, which is the multiple linear regression model, with student's cumulative GPA as the only predictor variable.
Abstract: Predicting student academic performance has long been an important research topic in many academic disciplines. The present study is the first study that develops and compares four types of mathematical models to predict student academic performance in engineering dynamics - a high-enrollment, high-impact, and core course that many engineering undergraduates are required to take. The four types of mathematical models include the multiple linear regression model, the multilayer perception network model, the radial basis function network model, and the support vector machine model. The inputs (i.e., predictor variables) of the models include student's cumulative GPA, grades earned in four pre-requisite courses (statics, calculus I, calculus II, and physics), and scores on three dynamics mid-term exams (i.e., the exams given to students during the semester and before the final exam). The output of the models is students' scores on the dynamics final comprehensive exam. A total of 2907 data points were collected from 323 undergraduates in four semesters. Based on the four types of mathematical models and six different combinations of predictor variables, a total of 24 predictive mathematical models were developed from the present study. The analysis reveals that the type of mathematical model has only a slight effect on the average prediction accuracy (APA, which indicates on average how well a model predicts the final exam scores of all students in the dynamics course) and on the percentage of accurate predictions (PAP, which is calculated as the number of accurate predictions divided by the total number of predictions). The combination of predictor variables has only a slight effect on the APA, but a profound effect on the PAP. In general, the support vector machine models have the highest PAP as compared to the other three types of mathematical models. The research findings from the present study imply that if the goal of the instructor is to predict the average academic performance of his/her dynamics class as a whole, the instructor should choose the simplest mathematical model, which is the multiple linear regression model, with student's cumulative GPA as the only predictor variable. Adding more predictor variables does not help improve the average prediction accuracy of any mathematical model. However, if the goal of the instructor is to predict the academic performance of individual students, the instructor should use the support vector machine model with the first six predictor variables as the inputs of the model, because this particular predictor combination increases the percentage of accurate predictions, and most importantly, allows sufficient time for the instructor to implement subsequent educational interventions to improve student learning.

300 citations