Lecture

Solid Kinematics: Gyroscope and Ball Dynamics

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the kinematics of rigid bodies, focusing on the gyroscope's different modes of rotation, including precession and nutation. It also explores the dynamics of a ball bouncing under a table and the motion of a Chinese spinning top.

In MOOC

Undeformable Solid Mechanics

This section deals with the mechanics of the undeformable solid. Whereas the entire course so far has been concerned with material points, we go beyond this model by considering any mass distribution that is totally rigid, i.e., undeformable. From the point of view of the art of modeling a physical system, we learn here how things get complicated when we refine a model. For most students, this is the chapter that brings them face to face for the first time with a so-called tensorial physical property: angul

Official source

Related concepts (20)

Rigid body dynamics

In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior.

Rigid body

In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light.

Kinematics

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.

Inverse kinematics

In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics.

Robot kinematics

In robotics, robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques.

Related lectures (64)

Solid Mechanics: Kinematics MOOC: Undeformable Solid Mechanics

Covers rigid body mechanics, defining positions, velocities, and accelerations of solid points.

Rigid Body with Fixed Axis and Gyroscopes

Explores gyroscopes, gyroscopic effects, and the dynamics of spinning objects with fixed axes.

Kinematics of Continuous Media

Explores the kinematics of continuous media, including deformation, rotation, and translation of particles and rigid bodies.

Kinematics and Dynamics of Rigid Bodies

Explores kinematics and dynamics of rigid bodies, including Euler angles and transfer theorems.

Gyroscope Applications in Medical Instrumentation