Dynamics and Dynamical Systems

List of symbols and notations

 A, B… points in space, curves, surfaces and solids A , B … matrices and operators A, B… a, b… units A , B … a , b … variables or modules of vectors  A ,  B …  a ,  b … vectors ˆ A , ˆ B … ˆ a , ˆ b … unit vectors  a ·  b scalar product of two vectors  a ×  b vector product of two vectors d a d x derivative of variable a with respect to x ˙ a , ¨ a … derivatives of variable a with respect to time ¯ a average value of variable a a acceleration  a acceleration vector a n normal (centripetal) acceleration a t tangential acceleration a x , a y , a z cartesian components of the acceleration C D drag coefficient cm centimeter; also, center of mass d moment arm of a force e Euler's number (base of the natural logarithms) E k kinetic energy E m mechanical energy ˆ e n , ˆ e t normal and tangential unit vectors ˆ e s , ˆ e v unit vectors in phase space  F force  F e elastic force  F f frictional force  F g weight (gravitational force)  F k ,  F s kinetic and static frictional forces F n , F t normal and tangential components of the force  F r resisting force in a fluid  g acceleration of gravity H hamiltonian function i imaginary number  − 1  I impulse I z , I cm moments of inertia with respect to the z axis and an axis through the center of mass ˆ ı , ˆ  , ˆ k cartesian unit vectors along the x , y and z axes J jacobian matrix J joule (SI unit of work and energy) k elastic constant kg kilogram (SI unit of mass) L angular momentum l effective length of a pendulum m mass m meter (SI unit of length)  M force moment of a couple  M P moment of a force about a point P N newton (SI unit of force)  N normal force N R Reynolds number ˆ n unit vector perpendicular to a plane  p quantity of motion (momentum)  r position vector r g radius of gyration R curvature radius of a trajectory R , θ , z cylindrical coordinates ˆ R , ˆ e θ , ˆ k unit vectors in cylindrical coordinates s position along the trajectory; also, deformation of a spring s second (SI unit of time) T period in a uniform circular motion or an oscillatory motion  u phase velocity U potential energy U e elastic potential energy U g gravitational potential energy V potential energy per unit mass v velocity  v velocity vector v x , v y , v z cartesian components of the velocity W work x , y , z cartesian coordinates α angular acceleration ∆ a increase of variable a during an interval of time ∆  r displacement vector ∆ s displacement along the trajectory η coefficient of viscosity θ rotation angle of the normal and tangential unit vectors λ eigenvalue of a matrix; also, Lagrange multiplier µ s , µ k coefficients of static and kinetic friction π ratio between the length of a circumference and its diameter ρ density ω angular velocity Ω angular frequency ° degree (unit of angle)