Transcribed Text
Computation
Projectile Motion
Atmospheric Effects
Consider simple ofai resistance proportional tothe projectiles velocity:
1bi
Furthermore,
consider
the
proportionality
depends
asfollows
Compare
the
trajectories
air
and
where
exponentially
decreases
Charged Particles
Cons themation of charged particle under Force the
magnetic fields.
Coriolis Effect
Conside the effects the motion of particles dueto the Earth's rotation
abouti axis. Using northsouth east west, updown choice faxis where the
position, velocity, and acceleration vectors canbe written as:

Suppose Earth rotates about axis with angular velocity vector n terms
of the angle of latitude, 6:
The Coriolis term for theacceleration observed from the noninertial reference frame of the form:
Include projectile motion and analyze the results.
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Gravity
Usethe Verlet Stormer algorithm tomodel satellite motion Arethe orbits stable? Consider different kinds of
orbits energy and angular momentum conserved over time?
Coupled Oscillators
Three Mass System
.
Analyze: linearly coupled systemofthree
"
masses shown inthefigure. Suppose alithe
masses are equal and k
4,
&
k3K Writea system equations o motion


DO
and usethe semiimplicit method to
00
numerically solve.
Describe normal modes of thesystem
Consider the weaklycoupled case where x "
Consid
Create simulation that shows (with lines connecting themas springs)
function ol
2 Dimensional Heat Equation
Create
ulation the 2D Heat Equation Boundan Condit
Neumann BC
This should bedoneon asquare initial temperature profiles fsimple shapes.
. You shoul make video evolution similar what shown here.
Wave Equation
Consider thefollowing initial boundan value Wave Equation
With fixed boundary conditions
w(t,0)
u(t,L)0
Arbitrary initi al conditions for both position velocity.
u(0,x)f(x)
u,(0,x)g(x)
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Usethe Central (CTCS) finite method approximation wherethe following
notation willbe followed:
xjAx
Wherei [0,1,2, such thatin Tand xx L The
Wave Equation becomes:
At2
Which
renders
Where
levels.
Meaning
knowing as well. Toget this
information,
Resulting in
2Atg(z)
Substitutin
recurrence
+2(1
Atg(x)
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The numerical solution However itis worth noting the choice of  1 is known as the
magic
time
step
and
the
Consider simple initial and start from rest i.e. g(x) 0
Create simulation shows the following BC's
o Dirichlet BC Both ends
Neumann BC Both ends ar free:
o Absorbing Boundary Condition (ABC). Both end totally absort energy. User  1 for this
Repeat for auniform initial velocity profile function: g(x)
The simulation should be similar that shown here (for fixed ends)
This material may consist of stepbystep explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning  misuse is strictly forbidden.
function [T,X]=SolvesemiImplctEuler(f,h,X0,n)
X=X0;
T=0;
%Loop to solve by Semiimplicit Euler
for i=1:n
dX=f(T(end),X(end,:));
Xn=X(end,:)+h*dX';
X=cat(1,X,Xn);
T=cat(1,T,T(end)+h);
end...