#PROGRAM-ID ChargeInEMfield
#VERSION 20240116
# A mass m with charge q>0 is located in a static electro-magnetic field [0,0,E], [0,-B,0].
# Find the trajetory
# Differential equation (Lorentz force): 
#   x'' = omega*z'
#   z'' = a*omega^2 - omega*x'
# good start settings are omega=0,92, a*omega^2=0,05

# coefficient definition
alias coefficient.1 -> omega_x # -omega for x'
coefficient.2 (+1) -> a*omega^2
alias coefficient(3) -> omega_z # omega for z'

# solving the DE
iintegrate (x'') -> -x'
iintegrate (-x') -> x

coefficient.omega_x (-x') -> -omega*x'
#cmultiply (-x', omega_x) -> omega*x'

iintegrate (a*omega^2, -omega*x') -> -z' # input is z''
iintegrate (-z') -> z
invert (-z') -> z'

coefficient.omega_z (z') -> omega*z'
#cmultiply (z', omega_z) -> omega*z'
assign omega*z' -> x''

output(x) -> out.x
output(z) -> out.z