Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

Data Link Layer
Framing See slides [here#page=6](KOM - lecture 4a - Itslearning.pdf) and more [here#page=3](KOM - lecture 4b - Itslearning.pdf). Ways of dividing data into packets for transmission. Character-oriented framing ![Pasted image 20230926123006.png](Pasted image 20230926123006.png) Escape characters are used to send the flag without it being interpreted as a flag by the receiver. Bit-oriented framing ![Pasted image 20230926123459.png](Pasted image 20230926123459.png) Flow and Error Control Protocols See [slides#page=14](KOM - lecture 4a - Itslearning.pdf). Automatic Repeat reQuest (ARQ) The sender listens for a confirmation packet from the receiver.
De kinematiske ligninger
De kinematiske ligninger $$ \begin{align} v = v_0 + at \s &\text{undlader: } x - x_0 \ x - x_0 = \frac{1}{2} at^{2}+ v_0t \s &\text{undlader: } v \ v^2 = v_0^2 + 2a(x-x_0) \s &\text{undlader: } t \end{align} $$ #fysik
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Degrees of Freedom
Degrees of Freedom How many directions/angles a joint can move in. To move to any point in space at any rotation 6 degrees of freedom are needed. #kinematics
Den Inverse af en Matrix
Den Inverse af en Matrix $$A^{-1} \cdot A = I$$ $I$ : [Identitetsmatrix#Identitetsmartix](Specielle Matricer) Løs ligningssystem med den Inverse Matrix Udgangspunkt: [ligningssystem](Linære Ligninssystemer) $$A\vec{x} = \vec{b}$$ “Dividerer med $A$” ($A^{-1}$ eksisterer kun hviss $\det(A) \neq 0$) $$A^{-1} \cdot A\vec{x} = A^{-1} \cdot \vec{b}$$ $$I\vec{x} = A^{-1} \cdot \vec{b} \arrow \vec{x} = A^{-1}\cdot \vec{b}$$ At finde den Inverse $$ A^{-1} =\left( \begin{array}{cccc} a_{11} & a_{12} & a_{13} & a_{14} \
Den retningsafledte
Den retningsafledte Hældningen i retning af $\vec{v}$. I et punkt $(x,y)$ og i en retning $\vec{v}$. $$D_{\frac{\vec{v}}{|\vec{v}|}} = \frac{\vec{v}}{|\vec{v}|} \bullet \nabla f(x,y)$$ #matematik #funktionafflerevariable
Densitet $$\rho = \frac{m}{R}$$ Enhed $$\frac{\text{kg}}{\text{m}^3}$$ #fysik
Det Komplekse Plan
Det Komplekse Plan [Calculus 9th.pdf#page=1084#page=1084](Calculus 9th.pdf) $$\C = \set{x + yi : x,y \in \R}$$ Plottes i et Argand diagram, med det reelle komponent ($Re(w)$) på “$x$-aksen” og den imaginære del ($Im(w)$) på “$y$-aksen”. #matematik
Determinanen for Matricer
Determinanen for Matricer Fortæller om en ($n\times n$) matrix $A$ har fuld [rang](Rang af Matrix). The matrix must be square. $$\det(A) \neq 0 \arrow \text{Fuld rang!}$$ For $2\times 2$ matricer $$M=\left( {\begin{array}{cccc} a & b \ c & d \ \end{array} } \right)$$ $$det(M) = detM = |M| = ad-cb$$ For $3\times 3$ matricer $$M= \left( {\begin{array}{cccc} a & b & c \ d & e & f \ g & h & i \end{array} } \right)$$ $$det(M) = |M| = a \cdot \left|\left( {\begin{array}{cccc} e & f \ h & i \ \end{array} } \right)\right| - b \cdot \left|\left( {\begin{array}{cccc} d & f \ g & i \ \end{array} } \right)\right| + c \cdot \left|\left( {\begin{array}{cccc} d & e \ g & h \ \end{array} } \right)\right|$$
DH-Parameters See the [slides](Lecture 7 - DH Parameters and Forward Kinematics.pdf). A standard for placing frames on a robot. Every joint can be describes as a combination of prismatic and revolute joints. Prismatic joint: Pure translation in one axis Revolute joint: Pure rotation in one axis Variables These values are derived for every link. $i$ denotes the link index. $a_{i-1}$: Link length, shortest distance between two joint axis. $\alpha_{i-1}$: Link twist, the angle between the axis around $a_{i-1}$.