The great Irish mathematician William Rowan Hamilton looms large in an intriguing but highly complicated project prepared by three students from CBS Synge Street, Dublin.
They used Hamiltonian maths to help reduce the simulation errors seen when modelling moving objects, for example an orbiting satellite.
Their approach is based on the use of a "hodograph", a mathematical concept developed by Hamilton in 1847, explains Adrian Chisa, (17). He, Keith Florea (16), and Sandeep Sihag (16), all fifth years at Synge Street, spent the last six to seven months working on the project, entitled "Estimation of simulation error in the Kepler problem using hodographs".
"We worked on it 10 hours a day some days," says Keith. "We enjoyed it - the physics was amazing."
The Kepler problem, named after the great Dutch astronomer, relates to the motion of a body attracted to a fixed point, a classic example being a geostationary satellite in orbit around the earth. This movement can easily be modelled using a mathematical algorithm based on Newton's second law of motion, but this can only provide an approximation of where a moving satellite will be. The question is how accurate is the approximation.
The three decided to tackle this problem in an attempt to reduce the simulation error by using Hamilton's hodographs. Conveniently, hodographs always form a perfect circle, no matter what shape of orbit is described.
They looked at existing simulation error- estimating methods and developed three of their own using Hamilton's hodographs.
They used an advanced computer programming language called Python to build and test their new algorithms. "Python is one of the best for working in three dimensions," Keith says.
All three students are originally from abroad. Keith is from Romania and has been here seven years. Sandeep has been here two years and comes from India. Adrian is also Romanian and has been in Ireland three years.
