What is Calculus of Variations? In general, developments in mathematics are motivated by the need for them in applications. Calculus of variations is no exception. In fact, it was first developed in 1969 when Johann Bernoulli asked the greatest mathematical minds of his time to solve the famous ‘brachistochrone problem’. This problem involves a bead […]

### The Future of Space Exploration

Space Travel, is the best of it over? Ever since we have seen the stars, mankind has been striving to discover how not only the world works, but how the universe functions as well. One of the most important ways of doing this is via space exploration, which as time has gone by has become […]

### Can a wave be represented by infinite discrete oscillators?

In this article I will find the equation of motion for an arbitrary number of discrete coupled oscillators (I will call “beads”) on a string. Then we will take the limit as the number of oscillators tends towards infinity, and see if the wave equation can be reproduced. If so it would be a good […]

### Does Neutron Star Collapse Violate Quantum Theory?

With the death of a star meaning that radiation pressure can no longer support the gravitational crush due to its large mass, Pauli’s exclusion principle maintains an equilibrium in what has now become a neutron star. Heisenberg uncertainty allows for a neutron star to undergo ultimate collapse, as a star becomes more massive momentum space […]

### Plasma Oscillations – “Langmuir Wave” approximation derivation

In a previous article we established an approximate estimate for the frequency of oscillations in a “cold plasma” because of small disturbances in the arrangement of the electrons and ions. In this article we will establish a much better model for oscillations in a plasma, which takes into consideration the fact that Plasmas tend to be […]

### Calculus Proof of Centripetal Acceleration Magnitude

In basic circular motion in physics we are given the following equation for the centripetal acceleration on a body moving in circular motion: However how can this be proved? Well, acceleration is a vector- so what we need to know is it’s magnitude and direction. The second part of which is obvious, it’s in the […]