Balder W. Holst

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

Integralregning - Basis
I integralregning finder man en funktions stamfunktion ($F(x)$). At integrere er det modsatte af at differentiere. Dvs. at $f(x)$ beskriver hældningen af $F(x)$. Integraler skrives således: $$\int f(x) \ dx = F(x) + k$$ Det er vigtigt at huske $dx$ i integralet. Det er bare en skrivemåde, men det er forkert ikke at skrive det. Noget andet der er vigtigt er at lægge $k$ til stamfunktionen. $k$ er bare en konstant, men den viser hvordan at man alligevel mister information når man integrere: hvis man kun har hældningen af en kurve, kan man godt generere den generalle form og hvor meget grafen stiger og falder, men man kan ikke finde startværdien for grafen.
0001/01/01 · Notes
Integration med Substidution
Integration med Substidution Kan anvendes på integraler på følgende form $$\int f(g(x)) \cdot k \cdot g'(x) \dx$$ Eksempel Dette er udtrykket vi forsøger at integrere. $$\int \sin(2t + \pi) dt$$ Vi definerer $u$ som den inderste funktion. Hvis det er en brøk er $u$ altid nævneren. $$u = 2t + \pi$$ Vi differentierer $$u' = \frac{du}{dt} = 2$$ Isolerer $dt$ $$dt = \frac{1}{2}du$$ Sætter $u$ og $du$ ind i formlen $$\int \sin(u) \cdot \frac{1}{2}du \arrows \frac{1}{2} \cdot \int sin(u) du \arrows \frac{1}{2} \cdot (-cos(u)+k)$$ Vi sætter ind på $u$’s plads $$\frac{1}{2} \cdot (-cos(2t+\pi)+k)\s = \s \frac{-cos(2t+\pi)+k}{2} $$ Dette er det integrerede udtryk.
0001/01/01 · Notes
Interfaces in C++
Interfaces in C++ A purely virtual class without variables. An Interface is an abstract class. Example class Creature { virtual get_info() =0; // Pure virtual } The =0 makes the function a pure virtual function. This means that get_info does not have to be immediately initialized.
0001/01/01 · Notes
Interfarans
Interfarans konstruktiv interfarans = når amplituden bliver forstærket som resultat af at to bølgetoppe mødes. Destruktiv interfarans = Når bølger udligner hinanden fordi bakketop og bakkedal mødes.
0001/01/01 · Notes
Interupts
Interupts An alternative to pooling. Allows the CPU to run a routine when an external device sends an interrupt request. The CPU will return to the normal program after the interrupt is executed. Microcontrolers usually have designated interrupt pins. When an interrupt is triggered, the interrupt handler adds the interrupt to a cue for execution. All interrupts can be enabled/disabled by the global interrupt (for atmega32A). AtMega32A Interrupts Interrupt Priority The lower the vector number, the higher the interrupt priority.
0001/01/01 · Notes
Inverse Kinematics
Inverse Kinematics “What should the states of the robot joints be, to get the end affecter to a certain position?" See slides. Hard because there may be zero or more solutions. Solutions See slide. Closed Form Solutions Exact mathematical solutions. Numerical Solutions Inexact solutions found by algorithms.
0001/01/01 · Notes
IPv4
IPv4 See slides. A 32-bit address. $$a.b.c.d/n$$ $n$: Number of bits in the prefix Error Reporting (ICMPv4) See slides.
0001/01/01 · Notes
IPv6
IPv6 Successor to IPv4. See slides. Addresses are 128 bit. Addresses can be either Unicast: Address of one specific computer Anycast: Address of a group of computers, only one will receive the packet. Multicast: Address of a group of computers, all will receive the packet. Benefits Better header format New options for additional functionality Possibility of extension Resource allocation support Global Unicast Addressing Global routing prefix: Website/Domain Subnet: Ex: Sections of a company Interface Identifier: The physical plug Special Addresses Compatible: Used when IPv4 devices want to communicate with each other Mapped: Used when IPv6 devices want to communicate IPv4 devices
0001/01/01 · Notes
Jacobian Matrix
Jacobian Matrix “The jacobian matrix is the matrix representing the best linear map approximation of > $f$> near > $(a,b)$> “ - > What is Jacobian?> $$ J(a,b) = \begin{bmatrix} \frac{\partial f_{1}}{\partial x_1}|_{(a,b)} & \frac{\partial f_{1}}{\partial x_2}|_{(a,b)} & \dots & \frac{\partial f_{1}}{\partial x_n}|_{(a,b)} \ \frac{\partial f_{2}}{\partial x_1}|_{(a,b)} & \frac{\partial f_{2}}{\partial x_2}|_{(a,b)} & \dots & \frac{\partial f_{2}}{\partial x_n}|_{(a,b)} \ \vdots & \vdots & \ddots & \vdots \ \frac{\partial f_{m}}{\partial x_1}|_{(a,b)} & \frac{\partial f_{m}}{\partial x_2}|_{(a,b)} & \dots & \frac{\partial f_{m}}{\partial x_n}|_{(a,b)} \ \end{bmatrix} $$
0001/01/01 · Notes
Jacobian Matrix for Robotics
Jacobian Matrix for Robotics The Jacobian matrix relates robot joint velocities to end-effector velocity. $$v = J(q) \cdot \dot{q}$$ $v$: Velocity of the end-effector (cartesian space) $J(q)$: The jacobian matrix, where $q$ is the current joint configuration $\dot{q}$: Velocity of the robot in joint space Each column tells how each joint contributes to the end-effector in cartesian coordinates. You can also find the joint velocities from the end-effector velocity like this: $$\dot{q} = J^{-1}(q) \cdot v$$ Note that THE INVERSE JACOBIN MAY NOT EXIST.
0001/01/01 · Notes