Conversion between quaternions and Euler angles

Computing Euler Angles: Tracking Attitude Using Quaternions

In this video we continue our discussion on how to track the attitude of a body in space using quaternions. The quaternion method is similar to the Euler Kinematical Equations and Poisson’s Kinematical Equations in that it consumes rate gyro information to compute Euler angles. However,

From playlist Flight Mechanics

Euler's Formula for the Quaternions

In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex

From playlist Math

CCSS What is the difference between Acute, Obtuse, Right and Straight Angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

Lecture 18: Rotation and How to Represent It, Unit Quaternions, the Space of Rotations

MIT 6.801 Machine Vision, Fall 2020 Instructor: Berthold Horn View the complete course: https://ocw.mit.edu/6-801F20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63pfpS1gV5P9tDxxL_e4W8O In this lecture, Prof. Horn focuses on rotations, including its properties, repre

From playlist MIT 6.801 Machine Vision, Fall 2020

Unity - lesson 11 - rotations

From playlist Unity game engine

Using difference of two angles with tangent to evaluate

👉 Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all

From playlist Sum and Difference Formulas

Lecture 06: 3D Rotations and Complex Representations (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

Learn how to evaluate the tangent of an angle usine sum and formula or two angles

👉 Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all

From playlist Sum and Difference Formulas

How to evaluate the difference of two angles for tangent

👉 Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all

From playlist Sum and Difference Formulas

What are reference angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

Determine the relationship between two angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

Lecture 20: Space of Rotations, Regular Tessellations, Critical Surfaces, Binocular Stereo

MIT 6.801 Machine Vision, Fall 2020 Instructor: Berthold Horn View the complete course: https://ocw.mit.edu/6-801F20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63pfpS1gV5P9tDxxL_e4W8O In this lecture, we will transition from solving problems of absolute rotation (w

From playlist MIT 6.801 Machine Vision, Fall 2020

Best Production Practices for Casual Games | Session 05 | #gamedev

Don’t forget to subscribe! This project series is about best production practices for casual games. Most game development projects fail. And, when they fail, hopes and dreams are squashed with them. But it doesn't have to be this way! We can learn a repeatable process for development su

From playlist Best Production Practices for Casual Games

3D Rotations and Quaternion Exponentials: Special Case

In this video, we'll understand 3D rotations from the point of view of vector analysis and quaternions. We will solve the problem of rotating a vector which is perpendicular to the axis of rotation in this video which will help us solve the general case in the next video. We will especiall

From playlist Quaternions

3D Rotations in General: Rodrigues Rotation Formula and Quaternion Exponentials

In this video, we will discover how to rotate any vector through any axis by breaking up a vector into a parallel part and a perpendicular part. Then, we will use vector analysis (cross products and dot products) to derive the Rodrigues rotation formula and finish with a quaternion point o

From playlist Quaternions

History of Science and Technology Q&A (June 2, 2021)

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Originally livestreamed at: https://twitch.tv/stephen_wolfram/ Outline of Q&A 0:00 Stream starts 2:35 Stephen begins the stream 3:07 What appeared first in math, complex

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

What are complementary angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

Pauli matrices vs. su(2) basis vs. quaternions

In this video we discuss Pauli matrices as base for hermitean 2x2 complex matrices, as relevant for modeling observables in quantum theory - but also for quantum mechanics, as demonstrated. You can find the text used in this video here: https://gist.github.com/Nikolaj-K/103f07367c116b64b56

From playlist Physics

Evaluating for the tangent of an angle using the difference formula, tan

👉 Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all

From playlist Sum and Difference Formulas