A- Plan of Attack:
- Do a research about catenary
shape curves
- Understand the relation between
least potential energy and the shape of the catenary
- Start a simple experiment
of a hanging chain starting with paper clips, such as 2 paper clips,
and try to find
a relation of the shape with respect to the lowest potential energy. Then
try 3
clips and also
try to find the relation between the shape and the lowest potential energy
for the
curve
- Now try to have the
whole chain and observe the shape
- Solve the ODE of the
curve and try to figure out the variables
- Apply the initial value
conditions to obtain the curve formula
- Use computer software
to plot the curve with the above formula
- Compare the plotted
curve to the shape of the hanging chain
- Write the report
B- Problems attempt to solve:
- Main problem is
to solve the ODE
- To get a feel
for how to solve the ODE, we approached the problem by trying to write the
equation
of a 2 paper clip chain in terms of the one variable ( angle of contact).
- Once we are done
with this, we work on deriving the equation
- Apply the initial
value conditions and be able to get to the integrating factors
- Next problem is
to compare the chain curve shape to the shape of the function we have derived
- We take several
plots and points of the plotted curve and compare it to the chain and see
how
they
should be identical
- Repeat the experiment
for different conditions( such as varying distance between the hanging points)