Consider simple ofai resistance proportional tothe projectiles velocity:
Cons themation of charged particle under Force the
Conside the effects the motion of particles dueto the Earth's rotation
abouti axis. Using north-south east west, up-down 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 non-inertial reference frame of the form:
Include projectile motion and analyze the results.
Usethe Verlet -Stormer algorithm tomodel satellite motion Arethe orbits stable? Consider different kinds of
orbits energy and angular momentum conserved over time?
Three Mass System
Analyze: linearly -coupled systemofthree
masses shown inthefigure. Suppose alithe
masses are equal and k
k3-K Writea system equations o motion
and usethe semi-implicit method to
Describe normal modes of thesystem
Consider the weakly-coupled case where x "
Create simulation that shows (with lines connecting themas springs)
2 Dimensional Heat Equation
ulation the 2D Heat Equation Boundan Condit
This should bedoneon asquare initial temperature profiles fsimple shapes.
. You shoul make video evolution similar what shown here.
Consider thefollowing initial boundan value Wave Equation
With fixed boundary conditions
Arbitrary initi al conditions for both position velocity.
Usethe Central- (CTCS) finite method approximation wherethe following
notation willbe followed:
Wherei [0,1,2, such thatin Tand xx -L The
Wave Equation becomes:
knowing as well. Toget this
The numerical solution However itis worth noting the choice of - 1 is known as 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)
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%Loop to solve by Semi-implicit Euler