Rico's Nerd Cluster

「离开世界之前 一切都是过程」

Linux - SSH and X Window System

X Window System, SSH, Static IP

SSH Generate an SSH Key: ssh-keygen -t rsa -b 4096. This will create ~/.ssh/id_rsa and optionally sets a passphrase Copy ssh onto a remote machine: ssh-copy-id username@rem...

Electronics - General Science Facts

Adiabatic Cooling

Adiabatic Cooling In an adiabatic process, the system does not gain or lose heat (Q=0Q=0), meaning that all changes in internal energy come from work done by or on the gas. For an ideal gas, the i...

Literature - The Wealthy Barber Notes

Financial Literacy

Roy’s Story “We all felt bad about Roy having to put off his dream of becoming a lawyer, but deep down we knew that he was doing the right thing. You got to be there when your family needs you,...

Electronics - General Electronics Notes

Encoders, Motors, Testing

Electronics EEPROM EEPROM (Electrically Erasable Programmable Read-Only Memory) is a type of non-volatile memory used in microcontrollers to store small amounts of data that must be preserved whe...

Electronics - Embedded Systems Notes

HAL

HAL vs SAL Hardware Abstraction Layer (HAL) is software that abstracts hardware-specific details from the application or higher-level software. It provides a unified API for accessing hardware fun...

Electronics - Communication Protocols

Encoding / Decoding, Error Checking (CRC)

Error Checking CRC GF(2) Math GF(2) is pronounced as “Galois Field 2”. Often used in cryptography, it’s a binary field that contains only 0 and 1 for error correction. Some properties of GF(2):...

Electronics - EMF and Eddy Current

Electromotive Force (EMF,电动势) In short, EMF is: 1 changing magnetic field -> induced voltage It’s characterized by the Faraday’s law: \[\begin{gather*} \begin{aligned} & \epsilon = -N \...

Math - Linear Fitting

Plane Fitting, Line Fitting

Given a group of points x_i = [x, y, z], how do we find a plane and a line that best fit them? Plane Fitting Points on a plane satisfy: \[\begin{gather*} \begin{aligned} & n^Tx + d = 0 \end{...

Math - SO(3) Perturbations

Left Perturbation, Right Perturbation, BCH Formula

Left and Right Perturbations Imagine we have a world frame, a car frame, and a pedestrian. Now the car has rotated from the car1 pose to the car2 pose. We assume the pedestrain has not moved: In ...

Math - Lie Group

Group Definition, Lie Group and Lie Algebras, Skew Matrices, Manifold, SO(3) Derivatives

Group Definition Group (Group) is an algebraic structure consisting of a set and an operation. Denote the set as A, and the operation as ⋅. Then, the group can be written as G=(A,⋅). Closure (...