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.

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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
2 weeks ago

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@Steven Chase thanks sir

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

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

Steven Chase - 2 weeks ago

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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)"

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

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

Steven Chase - 2 weeks ago

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@Steven Chase i stucked here

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@Neeraj Anand Badgujar 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

Steven Chase - 2 weeks ago

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@Steven Chase @Steven Chase which option should I choose here

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@Neeraj Anand Badgujar space delimited

Steven Chase - 2 weeks ago

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@Steven Chase @Steven Chase which option

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@Neeraj Anand Badgujar Just hit finish

Steven Chase - 2 weeks ago

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@Steven Chase @Steven Chase now where I have to go?

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@Neeraj Anand Badgujar Highlight columns B and C and then go to:

Insert - scatter chart - scatter with smooth lines

Steven Chase - 2 weeks ago

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

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@Steven Chase

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There it is

Steven Chase - 2 weeks ago

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

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@Neeraj Anand Badgujar 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

Steven Chase - 2 weeks ago

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@Steven Chase @Steven Chase yeah it is interesting

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

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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

Steven Chase - 2 weeks ago

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@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.
THANKS IN ADVANCE

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

Krishna Karthik - 1 week, 5 days ago

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

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Hey! You can check out this book.

Aaghaz Mahajan - 2 weeks ago

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@Aaghaz Mahajan Thanks bro for this book

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