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Engineering Mechanics
The chapter discusses the complexities of 3D rigid body motion, expanding on the concepts of angular velocity and moment of inertia beyond 2D frameworks. It highlights that angular velocity becomes a vector and that moment of inertia is represented by a tensor rather than a scalar. The discussion incorporates practical examples, such as conical motion, to illustrate how traditional 2D concepts fail and demonstrates the necessity for vector and tensor treatments to describe real-world scenarios.
Course Chapters
Vector Transformations and Newtonian Mechanics
Energy Methods, Force Fields & Central Forces
The chapter focuses on energy methods, force fields, and central forces, explaining the relationship between potential energy and force as the gradient of a potential function. It discusses conservative and non-conservative forces, analyzing scenarios such as central forces and their implications for angular momentum conservation in orbital mechanics. Additionally, it covers energy equations and diagrams, assessing orbital motion types based on energy and concluding with applications relevant to satellite maneuvers and Kepler's laws.
Non-Inertial Frames & Rotating Systems
The chapter discusses non-inertial frames of reference and introduces concepts such as pseudo-forces, rotating coordinate systems, and various accelerations related to rotating frames. It also covers practical applications, including natural phenomena influenced by the Coriolis effect and the Foucault pendulum, which demonstrates Earth's rotation. Finally, it encapsulates these ideas with useful formulas relevant to understanding motion in non-inertial frames.
Harmonic Oscillators & Damping
The chapter discusses harmonic oscillators, their motion characterized by a restoring force proportional to displacement, and the various forms of damping that affect oscillations. It introduces concepts such as forced oscillations and resonance, including their significance in engineering and real-world applications. Additionally, it explores energy considerations in damped and forced systems, providing essential formulas and insights.
Rigid Body Motion in the Plane
Rigid body motion encompasses several forms of movement, including translation and rotation in a plane. Angular kinematics describes the relationship between angular displacement, velocity, and acceleration. The chapter also delves into angular momentum and Euler’s laws of motion, providing a foundation for understanding the dynamics of rigid bodies.
Introduction to 3D Rigid Body Motion
The chapter discusses the complexities of 3D rigid body motion, expanding on the concepts of angular velocity and moment of inertia beyond 2D frameworks. It highlights that angular velocity becomes a vector and that moment of inertia is represented by a tensor rather than a scalar. The discussion incorporates practical examples, such as conical motion, to illustrate how traditional 2D concepts fail and demonstrates the necessity for vector and tensor treatments to describe real-world scenarios.