ELEMENTARY DYNAMICS

By N. HATIY

CONTENTS FUNDAMENTAL DEFINITIONS AND PRINCIPLES MOTION IN A STRAIGHT LINE UNIPLANAR MOTION WHERE THE ACCELERATIONS PARALLEL TO FIXED AXES ARE GIVEN UNIPLANAR MOTION REFERRED TO POLAR COORDINATES CENTRAL FORCES UNIPLANAR MOTION WHEN THE ACCELERATION IS CENTRAL AND VARYING AS THE INVERSE SQUARE OF THE DISTANCE TANGENTIAL AND NORMAL ACCELERATIONS: UNIPLANAR CONSTRAINED MOTION MOTION IN A RESISTING MEDIUM: MOTION OF PARTICLES OF VARYING MASS OSCILLATORY MOTION AND SMALL OSCILLATIONS MOTION IN THREE DIMENSIONS 10 MISCELLANEOUS THE HODOGRAPH: MOTION ON REVOLVING CURVES IMPULSIVE TENSIONS OF STRINGS 11 MISCELLANEOUS EXAMPLES I ON THE SOLUTION OF SOME OF THE MORE COMMON FORMS OF DIFFERENTIAL EQUATIONS CHAPTER FUNDAMENTAL DEFINITIONS AND PRINCIPLES 1 THE VELOCITY OF A POINT IS THE RATE OF ITS DISPLACEMENT, SO THAT, IF P BE ITS POSITION AT TIME T AND Q THAT AT TIME T +?T, THE LIMITING VALUE OF THE QUANTITY PQ ?T , AS ?T IS MADE VERY SMALL, IS ITS VELOCITY SINCE A DISPLACEMENT HAS BOTH MAGNITUDE AND DIRECTION, THE VE- LOCITY POSSESSES BOTH ALSO; THE LATTER CAN THEREFORE BE REPRESENTED IN MAGNITUDE AND DIRECTION BY A STRAIGHT LINE, AND IS HENCE CALLED A VEC- TOR QUANTITY 2 A POINT MAY HAVE TWO VELOCITIES IN DIFFERENT DIRECTIONS AT THE SAME INSTANT; THEY MAY BE COMPOUNDED INTO ONE VELOCITY BY THE FOLLOWING THEOREM KNOWN AS THE PARALLELOGRAM OF VELOCITIES; IF A MOVING POINT POSSESS SIMULTANEOUSLY VELOCITIES WHICH ARE REP- RESENTED IN MAGNITUDE AND DIRECTION BY THE TWO SIDES OF A PARALLELO- GRAM DRAWN FROM A POINT, THEY ARE EQUIVALENT TO A VELOCITY WHICH IS REPRESENTED IN MAGNITUDE AND DIRECTION BY THE DIAGONAL OF THE PAR- ALLELOGRAM PASSING THROUGH THE POINT THUS TWO COMPONENT VELOCITIES AB, AC ARE EQUIVALENT TO THE RESUL- TANT VELOCITY AD, WHERE AD IS THE DIAGONAL OF THE PARALLELOGRAM OF WHICH AB, AC ARE ADJACENT SIDES