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#### The paradigms of mechanics : a symmetry based approach.

(1996)

An overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three ...

#### Noether's theorem and first integrals of ordinary differential equations.

(1997)

The Lie theory of extended groups is a practical tool in the analysis of differential equations, particularly in the construction of solutions. A formalism of the Lie theory is given and contrasted with Noether's theorem ...

#### Ermakov systems : a group theoretic approach.

(1993)

The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) ...

#### Continuous symmetries of difference equations.

(2011)

We consider the study of symmetry analysis of difference equations. The original work done by
Lie about a century ago is known to be one of the best methods of solving differential equations.
Lie's theory of difference ...

#### Lie symmetries of junction conditions for radiating stars.

(2011)

We consider shear-free radiating spherical stars in general relativity. In particular we study the junction condition relating the pressure to the heat
flux at the boundary of the star. This is a nonlinear equation in ...