How to... export differential equations from Mechanical Expressions
 Mechanical Expressions is designed to give you the symbolic mechanics of an instantaneous snapshot in time.
You
can ask for the instantaneous acceleration in one or more constraints,
and the system assumes that those constraints are in fact free to
accelerate. It works out the appropriate acceleration(s).
In
the picture above, we have asked for the acceleration in the angle
constraint. As we have not specified an angular velocity, it is
assumed to be 0.
We can also output these accelerations in the form of differential equations, using Mechanics Output / Differential Equations Note
that rather than a single second order differential equation, we get a
system of first order differential equations along with initial
conditions.
Also note that we no longer consider the velocity to
be 0, except as an initial condition. So we have picked up extra
terms in the acceleration equation.
We would see these terms in the original diagram if we set an angular velocity. 
Anja Greer Conference
 Learn how to make eBooks for the iPad with interactive mathematical diagrams at the Anja S. Greer Conference on Mathematics, Science and Technology.
Philip
Todd will lead a 5 day workshop at the conference which will teach you
how to use Apple's iBook Author software in conjunction with Geometry
Expressions to create an interactive mathematical iBook.
Philip will share techniques he developed for his "24 Whimsical Clocks" iBook and for the interactive Euclid's Elements.
The conference takes place at the Phillips Exeter Academy June 22June 27 2014


Problem of the Month 
Another problem with an Archimedes connection.
The purple curve is the spiral whose polar definition is r(θ)=θ.
A is a point on the curve, O is the origin, and B is the intersection of the tangent at A with the perpendicular to OA.
What is the polar equation of the locus of B?
How about if the original curve is r(θ)=θ^2?
How about if the original curve is r(θ)=θ^n?
How about if the original curve is r(θ)=f(θ)?
An app which lets you explore this problem is here.

A Solution to January's Problem 
This month, a geometry problem which dates back to Archimedes.
CD is the diameter of a circle, and FB is perpendicular to CD. Tangents to the circle at D and B intersect at E.
Show that CE bisects BF.
Is there an analogous theorem for ellipses? How about hyperbolas and parabolas? An app which lets you explore this problem is here.
Solving
this problem with Geometry Expressions is straightforward if you are
prepared to accept the programs output. Just enter the drawing,
constraining the circle to have radius r and distance AF to be a.
Ensure the center of the circle is constrained to lie on the
diameter CD. Your model should look like this and the distances BG
and FG should be identical.
Please don't let this facile computer proof prevent you from looking for a geometric proof.
For
conics, an analogous theorem sets BF to be parallel to the tangent at D
rather than perpendicular to the circle's diameter (in the circle
these conditions are equivalent).
You can explore the analogous conic theorems here. 



