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Category Archives: Differential Equations
The hole through the middle of the Earth – revised transit time
In the previous post in this series I produced a table of acceleration due to gravity against depth from surface, based on the four layers of the Earth (Crust, Mantle, Outer Core, Inner Core), assuming a constant density for each layer. … Continue reading
Posted in Differential Equations, Excel, Newton, UDFs, VBA
Tagged Excel, hole through the middle of the earth, ODE Function, UDF, VBA
3 Comments
The hole through the middle of the Earth – acceleration
In my first go at modelling a ball falling through a hole through the middle of the Earth I assumed constant density, and hence the acceleration at any point was proportional to the distance from the centre. That is of course … Continue reading
Elegant solutions, Column buckling, and the hole through the middle of the Earth
The previous post presented some examples of solution of differential equations using an iterative process, including the simple harmonic motion problem of a ball falling through an evacuated hole through the middle of the Earth. The final example was concerned … Continue reading
Posted in Beam Bending, Differential Equations, Newton
Tagged column deflections, differential equations, Euler buckling
5 Comments
Using the AlgLib ODE (Runge-Kutta) Solver with Excel
Or to be more correct, the AlgLib Cash-Karp Solver, Cash-Karp being a refinement of the Runge-Kutta method of solving ordinary differential equations. Solution of differential equations is an iterative process requiring the repeated application of the solver routine followed by evaluation of … Continue reading
Posted in AlgLib, Beam Bending, Differential Equations, Excel, Maths, Newton, UDFs, VBA
Tagged AlgLib, buckling, Cash-Karp, differential equations, Excel. VBA, hole through the middle of the earth, Runge-Kutta, SHM, UDF
8 Comments
Elegant solutions, Simple Harmonic Motion, and the hole through the middle of the Earth
No, not the hole (beloved of conspiracy theorists everywhere) where our alien overlords keep their UFO’s, but rather the equally imaginary hole from Pole to Pole (beloved of physics teachers everywhere) where we can drop in objects and watch them travel … Continue reading
