# Kinematics from Numerical Integration

Launch a particle from ground level with some speed and some angle and compute the trajectory using numerical integration. This is a very simple example for those learning to program.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 import math # Constants g = 10.0 # gravity v0 = 20.0 # initial speed theta0 = math.pi/4.0 # initial angle dt = 10.0**(-5.0) # time step ####################################### # Initialize simulation t = 0.0 # time count = 0 # count for printing x = 0.0 # initial position y = 0.0 xd = v0*math.cos(theta0) # initial velocity yd = v0*math.sin(theta0) xdd = 0.0 # initial acceleration ydd = -g ####################################### # Run simulation while y >= 0.0: # run while object in flight # numerical integration # explicit Euler x = x + xd*dt # update position based on velocity y = y + yd*dt xd = xd + xdd*dt # update velocity based on acceleration yd = yd + ydd*dt xdd = 0.0 # constant accleration ydd = -g t = t + dt # advance time and count count = count + 1 if count % 1000 == 0: # print once every thousand simulation intervals print t,x,y 

The results were plotted in Excel

Note by Steven Chase
1 year, 1 month ago

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@Steven Chase thanks sir

- 1 year, 1 month ago

@Steven Chase sir i have also typed the the whole code ,but my code is not expressed as your code is expressed in brilliant ??

- 1 year, 1 month ago

You need three ticks and then "Python", and then code, followed by three more ticks

- 1 year, 1 month ago

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 print "import math #constant g = 10.0 #gravity v0 = 20.0 #initial speed theta0 = math.pi/4.0 #initial speed dt = 10.0**(-5.0) #time step ########################################## #Initial simulation t = 0.0 #time count = 0 #count for printing x = 0.0 #initial position y = 0.0 xd = v0*math.cos(theta0) #initial velocity yd = v0*math.sin(theta0) xdd = 0.0 #initial acceleration ydd = -g ############################################## #Run simulation while y >= 0.0: #run while object in flight #numerical integration #elpicit euler x = x + xd*dt #update position based on velocity y = y + yd*dt xd = xd + xdd*dt #update velocity based on acceleration yd = yd + ydd*dt xdd = 0.0 #constanrt acceleration t = t + dt #advance time and count count = count + 1 if count % 1000 == 0: #print once every thousand simulation intervals print (t,x,y)" 

- 1 year, 1 month ago

@Steven Chase sir can you please show a photo of your excel ,i am facing a bit of difficulty while plotting it in excel.

- 1 year, 1 month ago

You have to import the data from a text file and choose space-delimited format

- 1 year, 1 month ago

@Steven Chase i stucked here

- 1 year, 1 month ago

Have have to import the data in space delimited format, which you haven't done. Then highlight columns B and C.

Insert - Scatter - Scatter with smooth lines

- 1 year, 1 month ago

@Steven Chase which option should I choose here

- 1 year, 1 month ago

space delimited

- 1 year, 1 month ago

@Steven Chase which option

- 1 year, 1 month ago

Just hit finish

- 1 year, 1 month ago

@Steven Chase now where I have to go?

- 1 year, 1 month ago

Highlight columns B and C and then go to:

Insert - scatter chart - scatter with smooth lines

- 1 year, 1 month ago

I was going to that scatter only by mistake my arrow is at (other charts)

- 1 year, 1 month ago

- 1 year, 1 month ago

There it is

- 1 year, 1 month ago

@Steven Chase yes, Thank you sir
I don't think that anyone in the universe will help me like this you have helped me.

- 1 year, 1 month ago

You're welcome. And the cool part is that nowhere in the code is any parabola explicitly specified or coded. It just comes out of the numerical integration

- 1 year, 1 month ago

@Steven Chase yeah it is interesting

- 1 year, 1 month ago

@Steven Chase sir in the last 2nd step what is the meaning of that double equal to = = ??

- 1 year, 1 month ago

I single equals sign is used to declare the value of a quantity. A double equals sign is used to compare two quantities to see if they are equal

- 1 year, 1 month ago

@Steven Chase okay! thanks , can you please give me some questions or post for practicing numerical integration .
if you post it should be of E and M.

- 1 year, 1 month ago

Wow you're such a dedicated student. Really awesome to see passion and dedication :)

- 1 year, 1 month ago

@Steven Chase I want to learn monte Carlo, how can I learn??

- 1 year, 1 month ago

Hey! You can check out this book.

- 1 year, 1 month ago

@Aaghaz Mahajan Thanks bro for this book

- 1 year, 1 month ago