''' based on the discussion here https://code.sololearn.com/cKJ9au1K4F5y/?ref=app this code tries to unveil the best method to calculate the position of a body based on Netwon's laws. result: implement like this with small dt!! stick to the order p, v and a are updated. p=p+v*dt+a/2*dt**2 v=v+a*dt a=a+whatever is in your model t=t+dt ''' # WORK IN PROGRESS # constant acceleration # analytical solution: p=p0+v0*t+a/2*t**2 j=1 #m/s**3 a0=-32.333 #m/s**2 a=1 #m/s**2 v0=-50 #m/s p0=0 #m dt=0.02 #s t=0 pa=p0 pb=p0 pc=p0 pd=p0 va=v0 vb=v0 vc=v0 vd=v0 while t<100: pa=pa+va*dt va=va+a*dt vb=vb+a*dt pb=pb+vb*dt pc=pc+vc*dt+a/2*dt**2 vc=vc+a*dt vd=vd+a*dt pd=pd+vd*dt+a/2*dt**2 t=t+dt p=p0+v0*t+a/2*t**2 print('small dt, constant acceleration') print('%4f %4f <-'%(p, pa)) print('%4f %4f'%(p, pb)) print('%4f %4f <----'%(p, pc)) print('%4f %4f'%(p, pd)) print('-'*25) dt=0.5 #s t=0 pa=p0 pb=p0 pc=p0 pd=p0 va=v0 vb=v0 vc=v0 vd=v0 while t<100: pa=pa+va*dt va=va+a*dt vb=vb+a*dt pb=pb+vb*dt pc=pc+vc*dt+a/2*dt**2 vc=vc+a*dt vd=vd+a*dt pd=pd+vd*dt+a/2*dt**2 t=t+dt p=p0+v0*t+a/2*t**2 print('large dt, constant acceleration') print('%4f %4f'%(p, pa)) print('%4f %4f'%(p, pb)) print('%4f %4f <----'%(p, pc)) print('%4f %4f'%(p, pd)) print('\n'+'='*25+'\n') # linear acceleration # analytical solution: p=p0+v0*t+a0/2*t**2+j/6*t**3 dt=0.02 #s t=0 pa=p0 pb=p0 pc=p0 pd=p0 va=v0 vb=v0 vc=v0 vd=v0 aa=a0 ab=a0 ac=a0 ad=a0 while t<100: pa=pa+va*dt+aa/2*dt**2 va=va+aa*dt aa=aa+j*dt ab=ab+j*dt vb=vb+ab*dt pb=pb+vb*dt+ab/2*dt**2 pc=pc+vc*dt+ac/2*dt**2+j/6*dt**3 vc=vc+ac*dt+j/2*dt**2 ac=ac+j*dt ad=ad+j*dt vd=vd+ad*dt+j/2*dt**2 pd=pd+vd*dt+ad/2*dt**2+j/6*dt**3 t=t+dt p=p0+v0*t+a0/2*t**2+j/6*t**3 print('small dt, linear accel, constant jerk') print('%4f %4f <-'%(p, pa)) print('%4f %4f'%(p, pb)) print('%4f %4f <----'%(p, pc)) print('%4f %4f'%(p, pd)) print('-'*25) dt=0.5 #s t=0 pa=p0 pb=p0 pc=p0 pd=p0 va=v0 vb=v0 vc=v0 vd=v0 aa=a0 ab=a0 ac=a0 ad=a0 while t<100: pa=pa+va*dt+aa/2*dt**2 va=va+aa*dt aa=aa+j*dt ab=ab+j*dt vb=vb+ab*dt pb=pb+vb*dt+ab/2*dt**2 pc=pc+vc*dt+ac/2*dt**2+j/6*dt**3 vc=vc+ac*dt+j/2*dt**2 ac=ac+j*dt ad=ad+j*dt vd=vd+ad*dt+j/2*dt**2 pd=pd+vd*dt+ad/2*dt**2+j/6*dt**3 t=t+dt p=p0+v0*t+a0/2*t**2+j/6*t**3 print('large dt, linear accel, constant jerk') print('%4f %4f'%(p, pa)) print('%4f %4f'%(p, pb)) print('%4f %4f <----'%(p, pc)) print('%4f %4f'%(p, pd))

Position of body