Presentation is loading. Please wait.

Presentation is loading. Please wait.

Euler Angles. Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three.

Published by Modified over 9 years ago

Similar presentations

Presentation on theme: "Euler Angles. Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three."— Presentation transcript:

1 Euler Angles

2 Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three separate rotations about body axes 1) Rotation of  about e 3 axis. 2) Rotation of  about e 1 axis. 3) Rotation of  about e 3 axis.  These are the Euler angles. e1e1 e2e2 e3e3   

3 Euler Matrices  Any vector z can be rotated though the Euler angles.  Equivalent matrix operation is the product of three separate operations.

4 Full Rotation  Any rotation is then expressed with the three angles.

5 Matching Terms  The terms in the  matrix correspond to the components of the angular velocity vector.  The relationship between angular velocity and Euler angles comes from the S matrix.

6 Body Frame  The angular velocity in the body frame can be expressed in terms of Euler angles. x1x1 x2x2 x3x3

Download ppt "Euler Angles. Three Angles  A rotation matrix can be described with three free parameters. Select three separate rotations about body axesSelect three."

Similar presentations

Announcements. Structure-from-Motion Determining the 3-D structure of the world, and/or the motion of a camera using a sequence of images taken by a moving.

Announcements. Structure-from-Motion Determining the 3-D structure of the world, and/or the motion of a camera using a sequence of images taken by a moving.
Physics 430: Lecture 24 Euler Equations Dale E. Gary NJIT Physics Department.

Physics 430: Lecture 24 Euler Equations Dale E. Gary NJIT Physics Department.
P. Axelrad, D. Lawrence ASEN3200 Spring 2006 ATTITUDE REPRESENTATION l Attitude cannot be represented by vector in 3-dimensional space, like position or.

P. Axelrad, D. Lawrence ASEN3200 Spring 2006 ATTITUDE REPRESENTATION l Attitude cannot be represented by vector in 3-dimensional space, like position or.
Denavit-Hartenberg Convention

Denavit-Hartenberg Convention
ME751 Advanced Computational Multibody Dynamics Section 9.2 February 9, 2010 © Dan Negrut, 2010 ME751, UW-Madison “In England, if you commit a crime, the.

ME751 Advanced Computational Multibody Dynamics Section 9.2 February 9, 2010 © Dan Negrut, 2010 ME751, UW-Madison “In England, if you commit a crime, the.
Chris Hall Aerospace and Ocean Engineering

Chris Hall Aerospace and Ocean Engineering
3D Kinematics Eric Whitman 1/24/2010. Rigid Body State: 2D p.

3D Kinematics Eric Whitman 1/24/2010. Rigid Body State: 2D p.
1 Handout #17 Tennis racket demo Euler’s equations Motion of a free body No external torques Response to small disturbances  Tennis racket theorem  Nutation.

1 Handout #17 Tennis racket demo Euler’s equations Motion of a free body No external torques Response to small disturbances  Tennis racket theorem  Nutation.
Euler Rotation. Angular Momentum  The angular momentum J is defined in terms of the inertia tensor and angular velocity. All rotations included  The.

Euler Rotation. Angular Momentum  The angular momentum J is defined in terms of the inertia tensor and angular velocity. All rotations included  The.
Ch. 2: Rigid Body Motions and Homogeneous Transforms

Ch. 2: Rigid Body Motions and Homogeneous Transforms
Ch. 4: Velocity Kinematics

Ch. 4: Velocity Kinematics
3-D Geometry.

3-D Geometry.
Fictitious Force. Inertial Lagrangian  The Lagrangian is defined in an inertial system. Follows Newton’s lawsFollows Newton’s laws Equivalent in other.

Fictitious Force. Inertial Lagrangian  The Lagrangian is defined in an inertial system. Follows Newton’s lawsFollows Newton’s laws Equivalent in other.
Physics 3210 Week 12 clicker questions. If v is a vector in one frame and v is the same vector in a rotated frame, we showed that v=Av, where A is a rotation.

Physics 3210 Week 12 clicker questions. If v is a vector in one frame and v is the same vector in a rotated frame, we showed that v=Av, where A is a rotation.
Dr. Y.P. Daniel Chang Weidong Zhang Velocity Transformation Based Multi-Body Approach for Vehicle Dynamics Abstract: An automobile is a complex close loop.

Dr. Y.P. Daniel Chang Weidong Zhang Velocity Transformation Based Multi-Body Approach for Vehicle Dynamics Abstract: An automobile is a complex close loop.
Angular-Momentum Theory M. Auzinsh D. Budker S. Rochester Optically polarized atoms: understanding light-atom interactions Ch. 3.

Angular-Momentum Theory M. Auzinsh D. Budker S. Rochester Optically polarized atoms: understanding light-atom interactions Ch. 3.
Mechanics of Rigid Bodies

Mechanics of Rigid Bodies
Rotations and Translations. Representing a Point 3D A tri-dimensional point A is a reference coordinate system here.

Rotations and Translations. Representing a Point 3D A tri-dimensional point A is a reference coordinate system here.
Euler Equations. Rotating Vector  A fixed point on a rotating body is associated with a fixed vector. Vector z is a displacement Fixed in the body system.

Euler Equations. Rotating Vector  A fixed point on a rotating body is associated with a fixed vector. Vector z is a displacement Fixed in the body system.
Rotations. Space and Body  Space coordinates are an inertial system. Fixed in spaceFixed in space  Body coordinates are a non- inertial system. Move.

Rotations. Space and Body  Space coordinates are an inertial system. Fixed in spaceFixed in space  Body coordinates are a non- inertial system. Move.

Similar presentations

Ads by Google