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Monthly Archives: July 2020
The geometry of a second order differential equation, part 2
We start over with a general second order ordinary differential equation and this time we won’t impose any restrictions on the right-hand side. We express and which gives that The variables and denote velocity and are tangent space coordinates. The … Continue reading
The geometry of a second order differential equation, part 1
We start with a general second order ordinary differential equation and express and which gives that The variables and denote velocity and are tangent space coordinates. The variables and denote acceleration and are jet space (of curves) coordinates. Since the … Continue reading
The geometry of y”+y=0
In the differential equation we rewrite and get and with polarisation we get We read off the Christoffel symbols to be The connection one-form becomes and the curvature two-form is where is the covariant exterior derivative and means the ordinary … Continue reading
Curved Maths 