What is Euler angle: Definition and 11 Discussions

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering.

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1. The order of Euler Angle rotations for a top

Good Morning All. I have asked this before, but my post was not clear (my fault: I apologize). I hope this is more clear (please be patient as I try to get to the core of my confusion). In the first figure, below, the spinning top precesses as shown (well, it is not a animated jpg, but it...
2. I Understanding 3D Coordinate Rotations with Euler Angles

I'm trying to wrap my head around the concept. we use 3 rotations to transfer our regular cartesian coordinates (3 x,y,z unit vectors) to other 3 unit vectors. each rotation is associated with an angle. so far I'm good. but now I saw in Landau's and Lifshitz's "mechanics" book this thing...
3. A Integration with Euler angle of rotation matrixes

Hello, I was struggling with solving a specific integral. I know that I can rewrite the exponential matrices and the range of the three Euler angles. However, I am not sure I should I write in terms those three Euler angles.
4. A Euler Angles Transform: Rotating a Body in 3D Space

Only recently started to understand Euler angles and rotation matrices, and I am reasonably comfortable with the concepts already posted here. I am pretty sure I am missing something obvious, but I cannot figure out the way to solve this problem: A body in 3D space with a orientation defined by...
5. Linear Algebra Problem: Solving for Euler between two ordered bases

Homework Statement Linear Algebra Problem: Solving for Euler between two ordered bases I've got a problem I need to solve, but I can't find a clean solution. Let me see if I can outline the problem somewhat clearly. Okay, all of this will be in 3D space. In this space, we can define some...
6. Euler angles in latitude longitude space

In most physics introductions Euler angles(pitch, roll, yaw) are defined with respect to Cartesian coordinate system. If I chose not to use a Cartersian coordinate system but instead use a latitude, longitude and a proprietary vertical coordinate(and no back transformations to Cartersian...
7. Lack of Orientation of a Point Mass

The point mass (aka particle) is a fictional but useful concept. However, I have yet been able to find a definition of what exactly a point mass is. It is commonly accepted that a point mass does not have an orientation, and thus only 3 coordinates to determine its position are required (as...
8. Camera on Airplane: Extrinsic plus Intrinsic 3D Rotations?

Apologies up front for the long question … I have tried to be brief. I want to define camera angles for Google Earth (GE) when rotated about an aircraft yaw axis. The input is Latitude, Longitude, Altitude plus Heading, Pitch and Bank angles, actually coming from Flight Simulator. These drive...
9. Euler Angle from Body Frame to Inertial Frame

Hi, This is not really a homework problem, but a project I'm working on. So, I am trying to build a Simulink model for my quadcopter. I derived the equations of motion using the Newtown-Euler method in the body frame to get transnational and angular acceleration. For the transnational part, I...
10. Euler Angle transformation, help

I'm doing a research project currently and basically what I have is a camera measuring a probe. I have designed the camera to give the orientation of the probe using euler angles in the camera's frame of reference. This was working for most of my data, but now I need a 3-D visualization of what...
11. Eliminating the Euler Angle singularity without quaternions?

Hi all, I've formulated using Lagrangian formalism the equations of motion for a spinning top. I know about the gimbal lock/singularity that occurs at theta=0 and I was wondering if there was any other way to do it without dwelving into quaternions. Yogi published a paper "A Motion of Top...