#2-17-15

[spaceageunicorn]

There is something uniquely entertaining about watching a hockey game when you already know who's going to win, but the other team is so confident. It's just like oh baby, things are going to go so wrong for you in the third.

[whatsthevanaterwithyou-blog]

Final

[sylki]

15-462 Blog Post - Numerical Integration

This is a blog post for our 2/17/15 class in which we talked about Numerical Integration. (If you're just one of my regular followers, not my professor, and are seeing this, it's for a Technical Animation class I'm taking.)

We went over many different techniques in class, mostly going over the formulas. For my blog post I decided to organize and re-cap in one place some of the pros, cons, and real-world examples for the different integration techniques we talked about (mostly using the textbook and wikipedia to get a brief overview of each method). In doing so I hoped to gain a better understanding of how the methods differ from one another.

Euler: This is the most simple integration method. It is not time-reversible, as it depends on the value of the previous step to compute the next step. It is not very stable or very accurate, so for this reason it isn't used as much as other methods like Runge-Kutta, which have similar computational cost but more accurate results.

Runge-Kutta: Runge-Kutta methods are symmetrical with respect to each interval. They are a lot more stable and accurate than Euler. in RK4 specifically, though there is a lot of computation on each step, it increases accuracy so that larger time steps can be taken and overall computational cost is less than with naive Euler.

Implicit Euler: This is also known as the backward Euler method. The implicit method finds a position whose derivative can update the current value to the new value at the next time step. While it takes more time to solve this equation than the forward Euler, it is more stable and larger time steps can be taken, so in the long run computational savings occur, just like in Runge-Kutta.

Semi-implicit Euler: Unlike Euler, it is symplectic, meaning it conserves energy of dynamic systems. It is more stable and computationally costs less as well. It is used in many physics engines because it has many desirable qualities.

Leapfrog: One of this method's strengths is that it is time-reversible, meaning you can integrate both forward and backward in time steps. It is also symplectic. For this reason it is often used specifically in orbital dynamics, since other integration schemes like RK4 don't conserve energy. It is also used in gravity simulations, though RK4 is more commonly used here.

Verlet: Verlet has been used to calculate trajectories of particles in molecular dynamics simulations, calculate the orbit of Halley's Comet, and study the motion of electrical particles in a magnetic field. The Verlet method can also be modified to create a damping effect which can be used to emulate air friction in video games. Like Leapfrog, it is time-reversible and symplectic. It is also stable and does not require a whole lot more computation than the Euler method.

[candoblue]

The need to become heavily intoxicated has not existed for such some time until now.

[forgetyoursingalongsandlullabies]

5 positive things

Aisha gave me the best ever valentine lol

Went and got Filipino food after school. I haven't eaten dinuguan since August omg its the best

Finally got my cat to sit still to get his flea collar on

Watched the new Sleepy Hollow

Finished my homework before midnight

[all-things-bexx]

I give up...I can't breathe....I just want to be done....

[luckyleolion]

Im jus going to cry now. Like honestly what....I got an 80....an 80....oh my god....how....oh my god....this is so bad....an 80....im going to have to take this class again....oh my god.....this is so bad....my stomach hurts....oh my god....what the fucking hell this is pissy. Im jus ahhhhhh oh my fucking are you son of a bitch son of a fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck fuck ahhhhhhhhhbhh!!! 1i can't believe this I jus how the fuck like are you serious he better drop a quiz and test grade to be honest like oh my fucking god im mad now. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. Wow. I can't believe this shit. Son of a bitch. Fuck. Fuuuuuuuuuuckkkkkkkkkkk. Oh my fucking god. Fuuuuuuuuuckkkkkkkkkk

[luckyleolion]

anyway so the thought of my friend going to my college would be so so awesome!!! like i think it would be because that would mean that he is staying in town probably staying in the neighborhood and we could hang out on weekends that is if we dont see each other at school and maybe if we can work it out i can have a class with him like speech or something! and it would be totes cute! and this guy who we hangout with sometimes is also thinking about going to my school and that would mean he is staying too and that would be pretty cool in all honesty. there is a gas station and a little fast food place being built like right around the corner and me and my friend are thinking about going there whenever it gets fully built and we could be like regulars and it would be awesome. like this could be a really good year coming up and although this past year actually wasn't bad it was a little bland to be honest. but i really hope he comes to my school but i really dont want to push it on him so im not saying anything. but it would be so amazing! ugh!!!! that's like super exciting!!! like i wish!!!!!