Rodrigues' rotation formula

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

Derivation of Rodrigues’ Rotation Formula

In this video we explain and derive Rodrigues’ Rotation Formula. This functions describes how to rotate an arbitrary vector about another arbitrary axis of rotation. This has applications to orbital mechanics, computer graphics, rigid body kinematics, and dynamic system simulation. This

From playlist Flight Mechanics

Determining clockwise vs counter clockwise rotations

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

Euler Angles and the Euler Rotation Sequence

In this video we discuss how Euler angles are used to define the relative orientation of one coordinate frame to another. Topics and Timestamps: 0:00 – Introduction and example 2:34 – The Euler Rotation Sequence 16:10 – Matlab animation showing rotation sequence 21:03 – The direction cos

From playlist Flight Mechanics

How to determine the rotation of a heart

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

Euler's formulas, Rodrigues' formula

In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5

From playlist Algebra

What is the difference between rotating clockwise and counter clockwise

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

Expressing Vectors in Different Frames Using Rotation Matrices

In this video we develop notation to express a vector in different reference/coordinate frames. We then investigate how to use rotation matrices to translate from a vector expressed in one frame to this same vector expressed in another frame. Topics and time stamps: (0:43) – Introduction

From playlist Flight Mechanics

How to determine the points of a triangle rotated 90 degrees counter clockwise

👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will

From playlist Transformations

Rotation of Matrices

In this video, I have emphasized on the concept of rotation of matrices and what it means in the real world. This video is part of the Summer of Math Exposition 2. important links: https://math.stackexchange.com/questions/197772/generalized-rotation-matrix-in-n-dimensional-space-around-n

From playlist Summer of Math Exposition 2 videos

PROOF That V = Rω!!!

Using Calculus In ROTATIONAL Mechanics!!! #Physics #Mechanics #College #Motion #NicholasGKK #Shorts

From playlist General Mechanics

Vector Derivatives (the Equation of Coriolis) and the Angular Velocity Vector

In this video we develop the Equation of Coriolis which describes how a vector in a rotating reference frame changes from the perspective of an observer in a non-rotating reference frame. We will see that this is related to the angular velocity vector describing the relative motion of the

From playlist Flight Mechanics

Coriolis Effect Demonstration (with Drones)

We demonstrate how rotating reference frames give rise to the Coriolis effect and centrifugal acceleration. In this video, we approach this as a simple physics demonstration and examine several scenarios where the Coriolis effect manifests. In a separate video, we provide a rigorous anal

From playlist Physics Demonstrations

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

Rules, Rule-Breaking, and French Neoclassicism: Crash Course Theater #20

Everyone knows, you need a bunch of rules to make good theater. That's what the French thought in the 17th century, anyway. The French Neoclassical revival had a BUNCH of French playwrights following a bunch of rules. Unsurprisingly, some of the most interesting plays of the era broke thos

From playlist Crash Course Theater and Drama

How to Calculate a Rotation Matrix | Classical Mechanics

In this video, we will show you how to calculate the rotation matrix for any given rotation. To do so, we will assume a passive rotation, that is we rotate our basis vectors. 00:00 Introduction 00:34 Example 01:25 Proof Follow us on Instagram: https://www.instagram.com/prettymuchvideo/

From playlist Classical Mechanics

The virgin rotation matrix vs. the Chad axis–angle

In this video I talk about a lot of the representations for rotations in two and three dimensions. This is also really a Lie-algebra/Lie-group motivation video. Here's the text used: https://gist.github.com/Nikolaj-K/907e0ea3cc958c483572950b746e0145 Here's relevant links: https://en.wikip

From playlist Algebra