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

Andenordensdifferentialligninger [Dæmpede Svingninger - Differentialligning](Dæmpede Svingninger - Differentialligning) [Andenordens inhomogene differentialligninger](Andenordens inhomogene differentialligninger) Begyndelsesværdier $$y'' + y' - 2y=0, \s y(0),\s y'(0)=-1$$ $$r^{2}+r-2=0 \arrow = \frac{-1\pm\sqrt{1+8}}{2}=\begin{cases} r_1=1\ r_2=-2 \end{cases}$$ $$y=A \cdot e^{x}+B\cdot e^{-2x}$$ $$y'=A \cdot e^{x} -B \cdot 2 \cdot e^{-2x}$$ Indsætter værdier $$ \begin{align} y(0)=A \cdot e^{0} + B \cdot e^{-2 \cdot 0} = 0 &\arrow A+B=2 \ y'=A \cdot e^{x} -B \cdot 2 \cdot e^{-2x} &\arrow A-2B=-1 \end{align} $$ Trækker de to ligninger fra hinanden $$(A+B)-(A-2B)=2-(-1) \arrow A=1,\s B=1$$
Angle-Set Conventions
Angle-Set Conventions Ways to rotate around an axis with [rotational matrices](Rotational Matrices). Summary $$R_{\text{euler}}(x', y', z') = R_{\text{fixed}}(z, y, x) \Rightarrow R_{x'} \cdot R_{y'} \cdot R_{z'} = R_{x} \cdot R_{y} \cdot R_{z}$$ #Fixed Angles#Fixed Angles $$ R_Z(45\deg) \cdot \ ^\text{Base}_\text{TCP}R \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{base} z-axis} $$ #Euler Angles#Euler Angles $$ ^\text{Base}_\text{TCP}R \cdot R_Z(45\deg) \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{toolhead} z-axis} $$
Anti Aliasering Filter
Anti Aliasering Filter A filter cutting off all frequencies that are larger than double the sampling frequency. Without an anti aliasing filter, high frequencies will be mapped to low frequencies when [impule](Impulse Sampling)- and [pulse sampling](Pulse Sampling). Insufficient Sampling ![Pasted image 20230921084342.png](Pasted image 20230921084342.png) #signalprocessing
Approximation Måder at estimere funktioner, der gør dem nemmere at regne med. Noter list from #approximation sort file.name #subject #matematik
Arbejde $$W = \vec{F} \bullet \Delta\vec{r}$$ $$W_F=F \cdot \Delta x \cdot \cos(\theta)$$ $W_F$ : Arbejde $F$ : Kraften $\Delta x$ : Ændring i position $\cos(\theta)$ : Bruges til at finde $x$-komposanten af $F$. Arbejde og [Potentiel Energi](Potentiel Energi) $$W = -E_{pot}$$ Arbejdet udført på et objekt er lig objektets ændring i [Kinetisk Energi](Kinetisk Energi). $$W_{net}=\Delta E_{kin}$$ Udregning af Arbejde ved variable Kræfter Vi deler distancen op i uendelig små distancer, hvor vi antager at kraften er konstant.
ARP Packet
ARP Packet Ask all the nodes where a target ip is. The node that hosts the target ip sends a unicast packet back to the sender, letting it know of its location in the network. Example ARP Packet ![Pasted image 20230919124037.png](Pasted image 20230919124037.png) Format ![450](Pasted image 20230919123907.png) #datacommunication #TCP-IP
Arrays in C++
Arrays in C++ C++ Arrays This is the c++ way of doing arrays. It is a lightweight wrapper for c-style arrays. std::array<type, size> Example: #include <iostream>#include <array> int main() { std::array<std::string, 3> myArray = {"en", "to", "tre"}; std::cout << "Length of array: " << myArray.size() << std::endl; for (std::string e : myArray) { std::cout << e << std::endl; } return (0); } Old C-style Arrays This is the C way of doing arrays.
Assembly See atmel-0856-avr-instruction-set-manual.pdf#page=10#page=10. The Stack If you are using the stack, the stackpointer should be initialized like this: LDI R16, HIGH(RAMEND) OUT SPH, R16 LDI R16, LOW(RAMEND) OUT SPL, R16 PUSH Push data to the stack and decrease the stack pointer by one. PUSH register POP Load data from the stack and increase the stack pointer by one. POP register Subrutines “Functions” in assembly. CALL Call a subrutine. The stack pointer is reduced by two.
Assumptions of Kinematics
Assumptions of Kinematics Ignore any forces #kinematics
At Gøre Prøve
At Gøre Prøve At gøre prøve er en måde at teste om en bestemt funktion, er en løsning for en given differentialligning. Eksempelvis kunne man spørge: er $f(x) = 2e^{16x}$ en gyldig løsning på differentialligningen $y' = 16y$? Det første skridt mod at besvare spørgsmålet er at differentiere funktionen. $$f'(x)=32e^{16x}$$ Vi kan nu sætte vores $f(x)$ og $f'(x)$ ind i differentialligningen $$y = 16y \s f'(x) = 16 \cdot f(x) \s 32e^{16x} = 16 \cdot 2e^{16x} \s 32e^{16x} = 32e^{16x}$$