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

Andenordens inhomogene differentialligninger
Andenordens inhomogene differentialligninger $$ay''+by'+cy=f(x)$$ $a, b, c$ : Konstanter. Find Løsningen! Løs den homogene differentialligning. (se Dæmpede Svingninger - Differentialligning) $$ay''+by'+cy=0$$ Kald løsningen $y_h$ Løsningen er nu giver ved $$y=y_h+y_p$$ hvor $y_p$ er den partikulære løsning. Gæt $y_p$ fra kvalificeret gæt. Kvalificerede gæt: $f(x)$ Gæt $P_n(x)$ Et generelt n’te grads polynomium $e^{rx}$ $A \cdot e^{rt}$, $A \in \R$ on konstant $\cos(ax)$ $A \cdot \cos(ax)+B\cdot \sin(ax)$, hvor $A, B \in \R$ og konstante.
Andenordensdifferentialligninger Dæmpede Svingninger - Differentialligning 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. 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 $$ R_Z(45\deg) \cdot \ ^\text{Base}_\text{TCP}R \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{base} z-axis} $$ Euler Angles $$ ^\text{Base}_\text{TCP}R \cdot R_Z(45\deg) \Rightarrow \text{Rotate toolhead } 45 \deg \text{round the \textit{toolhead} z-axis} $$
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- and pulse sampling. Insufficient Sampling
Approximation Måder at estimere funktioner, der gør dem nemmere at regne med. Noter list from #approximation sort file.name
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 $$W = -E_{pot}$$ Arbejdet udført på et objekt er lig objektets ændring i 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.
Arc Length
Arc Length You can find the length of an arc by adding the small length of the infinity small vectors making up the arc. $$\vec{r(t)} = f(t) i + g(t) j + h(t) k$$ $$|r'(t)| = \sqrt{f'(t)^{2} + g'(t)^{2} + h'(t)^{2}}$$ $$L=\int_{\alpha}^{\beta} |r'(t)| dt$$
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 Format
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. 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.