1c

import math
import numpy as np
from matplotlib import pyplot as plt
##Constants
alpha = 1
m = 1
Vwater = np.array([1,1])
#Vwater(X)

def eq2(X):
    x=X[0]
    y=X[1]
    R=math.sqrt(x**2+y**2)
    T=24*60*60 #setter perioden til 1 døgn i sekunder
    factor=2*math.pi/T
    Y=[x,y]
    Y[0]+=factor*(-y)
    Y[1]+=factor*x
    return Y

def eq1(alpha,m,X,Xdot):
    Ydot = trapezoid()
    Y = trapezoid()

def trapezoid(X,Xdot,h):
    Wip1euler = euler(X,Xdot,h)
    Wip1 = np.array([0,0])
    Wip1 = X + h/2*()
    #Y[0] = X[0] + h/2*(deriv i pkt + deriv i neste pkt)
    #Y[1] =
    return 0

X = np.array([100,0])
Xdot = np.array([0,0])
h = 0.1

def f1dummy(X):
    alpha/m
    return np.array([1,1])
##
def XdotEuler(X,Xdot,h):
    return Xdot + h*alpha/m*(Vwater-Xdot) #Vwater som funksjon av X (ved rett tid)

def euler(X,Xdot,h):
    Wip1 = X + h*XdotEuler(X,Xdot,h)
    return Wip1

def XdotTrapezoid(X,Xdot,h): #deriv her         #deriv ved neste steg fra euler
    return Xdot + h/2*(alpha/m*(Vwater-Xdot) + alpha/m*(Vwater-XdotEuler(X,Xdot,h)))
    #Vwater(euler(X,Xdot,h)) for å finne farten ved t(i+1)

def trapezoid(X,Xdot,h):
    return X + h/2*(XdotTrapezoid(X,Xdot,h) + XdotTrapezoid(euler(X,Xdot,h),XdotEuler(euler(X,Xdot,h),Xdot,h),h)
##
##
##
def euler(X,Xdot,h): #gir neste posisjon
    Wip1 = X + h*Xdot
    return Wip1
#def nextXdot():
    Xdot + h*alpha/m*(Vwater-Xdot) #Vwater som funksjon av X (ved rett tid)

def XdotTrapezoid(X,Xdot,h): #deriv her         #deriv ved neste steg fra euler
    return Xdot + h/2*(alpha/m*(Vwater-Xdot) + alpha/m*(Vwater-(Xdot + h*alpha/m*(Vwater-Xdot))))
    return Xdot + h/2*(alpha/m*(Vwater-Xdot) + alpha/m*(Vwater-(Xdot + h*alpha/m*(Vwater-Xdot))))
    return Xdot + h/2*(alpha/m*(Vwater-Xdot) + alpha/m*(Vwater-(Xdot + h*alpha/m*(Vwater-Xdot))))

def trapezoid(X,Xdot,h):    #derivert i neste punkt vi får fra Euler (DET er trapes!)
    return X + h/2*(Xdot + (Xdot + h/2*(alpha/m*(Vwater-Xdot) + alpha/m*(Vwater-(Xdot + h*alpha/m*(Vwater-Xdot))))))

#alt i det siste leddet skal skje i neste posisjon som beregnet via euler
def dummy():
    Wip1 = np.array([1,2,3,4])
    print(Wip1)
    Wip1 = Wip1 + Wip1*2
    print(Wip1)

def main():
    #print(X)
    #print(Xdot)
    #print(euler(X,Xdot,h))
    #dummy()
    #print(euler(X,Xdot,h))
    return 0

main()
#fjern factor og T fra loopen
#Lag en syntaksfil. X = xvector i og Y er xvector i+1