Mathematical Modelling of Meteoroid Streams

Preface<div>1. Introduction</div><div>1.1 Mathematical modelling in general</div><div>1.2 On history of meteoroid stream modelling</div><div>2. Initial stage: the model stream generation</div><div>2.1 Choice of the ejection point on the reference orbit</div><div>2.1.1 Ejection in one point</div><div>2.1.2 Ejection along the orbit</div><div>2.2 Ejection velocity vector</div><div>2.2.1 Coordinate system</div><div>2.2.2 Isotropic ejection</div><div>2.2.3 Ejection in a cone</div><div>2.2.4 Subsolar point and the cosine ejection</div><div>2.2.5 Ejection speed</div><div>2.3 Calculation of the model meteoroid orbit</div><div>2.4 A simple model: the nonperturbed stream</div><div>3. The model stream evolution</div><div>3.1 Numerical integration</div><div>3.2 Analytical solution</div><div>3.3 How to take into account the radiation pressure force</div><div>3.4 How to take into account the Poynting–Robertson drag force</div><div>4. The end stage: the model stream now</div><div>4.1 Meteoroids registration on the Earth</div><div>4.2 The activity profile of the model meteor shower</div><div>4.3 Model radiants</div><div>4.4 Mass distribution in the model shower</div><div>5. Visualization of the results</div><div>5.1 Cross‐section in the ecliptic plane</div><div>5.2 Cross‐section perpendicular to the velocity vector</div><div>6. Application to real streams, analysis</div><div>6.1 Physical model of a meteoroid stream</div><div>6.2 Age of a meteoroid stream</div><div>6.3 Observations — the base for modelling</div><div>Notation conventions</div><div>Glossary</div><div>References</div><div>APPENDICES</div><div>A1. Transition from the rectangular coordinates to the orbital elements and back</div><div>A2. Transition between the coordinate systems</div><div>A3. Random number generation</div>