sMark Notes [DRAFT]
Mark M. Tobenkin’s Notes on Math and Other Topics
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04
Jan 2021
Integration on SO(3)
This post is about numerical integration on $SO(3)$, i.e. how to approximate the solution of: $$ \frac{d}{dt} C(t) = C(...
03
Jan 2021
Derivation of the Bortz Equation
This post gives a derivation of the [Bortz Equation](https://ntrs.nasa.gov/citations/19700013316), which is useful for ...
03
Jan 2021
Directional Derivative of $\exp$ on $\mathfrak{so}(3)$
This post is about finding the directional derivative: $$ \left . \frac{d}{d\lambda} \exp([\omega + \lambda w]\_\times)...
03
Jan 2021
$SO(3)$ Integrals
This post is about a family of integrals that are important when computing [state transition matrices]({{<ref "posts/sy...
31
Dec 2020
$\mathfrak{so}(3)$ Power Series
This post is about power series of the form: $$ \alpha_0 I + \sum_{n=0}^\infty \alpha_n [v]\_\times^n. $$ Assuming $v...
28
Dec 2020
State Transition Matrices
This post has a few tricks for deriving [state transitions matrices](https://en.wikipedia.org/wiki/State-transition_mat...
28
Dec 2020
Matrix Exponential Directional Derivative
We can find a general expression for the derivative: $$ \left . \frac{\partial}{\partial \lambda} \exp(A + \lambda \De...
27
Dec 2020
Useful Properties of $\mathfrak{so}(3)$
This note reviews important properties of what you might call the cross product matrix. For a vector $u \in \mathbb{R}^3...