Outline
● Higher-order functions and lists in Haskell recap
● User-defined types in Haskell recap
● Exercise: N-body simulation
N-body simulation: prerequisites
Exercise 5.1.
Define type Body to represent state of a given body: mass, 2D position, and velocity vector. Implement function renderBody to render a given body. Define some bodies (e.g., earth, moon, or sun).
Exercise 5.2.
Define type System to represent a system (collection) of bodies for simulation. Implement function renderSystem to render an entire system. Define a sample system (e.g., earth+moon or earth+sun).
N-body simulation: moving bodies
Exercise 5.3.
Define a function moveBody :: Double -> Body -> Body that updates body’s position based on its velocity and given time (in seconds).
Exercise 5.4.
Define a function updateSystem to update positions and velocities of all bodies in a given system over a given time (in seconds).
You can use the following snippet for more details: https://code.world/haskell#P__XNId0wAKIATT95b_Idzw
N-body simulation: computing gravity effect
Exercise 5.5.
Define a function gravityAcc :: Body -> Body -> Vector that computes the acceleration that second body gets as the gravitational effect of the first body. Use the following formula:
Exercise 5.6.
Define a function applyGravity :: Double -> [Body] -> Body -> Body that computes the combined gravity effect of a collection of bodies on a given body over given time (in seconds) and returns the new state of the body.
N-body simulation: putting things together
Exercise 5.7.
Define a function updateBody :: Double -> [Body] -> Body -> Body that updates both position and velocity of a body. Use this function in updateSystem to make the entire simulation work with gravity.
