Galilean moons century when other inner moons were discovered, and Marius' names became widely used. Galileo was able to develop a method of determining longitude based on the timing of the orbits of the Galilean moons. The times of the eclipses of the moons could be precisely calculated in advance, and compared with local observations on land or on ship to determine the local time and hence longitude. The main problem with the technique was that it was difficult to observe the Galilean moons through a telescope on a moving ship; a problem that Galileo tried to solve with the invention of
Newtonian dynamics constraints look like scalar equations of the form Constraints of the form () are called holonomic and scleronomic. In terms of the radius-vector formula_10 of the Newtonian dynamical system () they are written as Each such constraint reduces by one the number of degrees of freedom of the Newtonian dynamical system (). Therefore the constrained system has formula_16 degrees of freedom. Definition. The constraint equations () define an formula_17-dimensional manifold formula_18 within the configuration space of the Newtonian dynamical system (). This manifold formula_18 is called the configuration space of the constrained system. Its tangent bundle formula_20 is called the