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1 #PROGRAM-ID ChargeInEMfield

2 #VERSION 20240116

3 # A mass m with charge q>0 is located in a static electro-magnetic field [0,0,E], [0,-B,0].

4 # Find the trajetory

5 # Differential equation (Lorentz force):

6 # x'' = omega*z'

7 # z'' = a*omega^2 - omega*x'

8 # good start settings are omega=0,92, a*omega^2=0,05

10 # coefficient definition

11 alias coefficient.1 -> omega_x # -omega for x'

12 coefficient.2 (+1) -> a*omega^2

13 alias coefficient(3) -> omega_z # omega for z'

15 # solving the DE

16 iintegrate (x'') -> -x'

17 iintegrate (-x') -> x

19 coefficient.omega_x (-x') -> -omega*x'

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

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

23 iintegrate (-z') -> z

24 invert (-z') -> z'

26 coefficient.omega_z (z') -> omega*z'

27 #cmultiply (z', omega_z) -> omega*z'

28 assign omega*z' -> x''

30 output(x) -> out.x

31 output(z) -> out.z