Classical and analytical mechanics : theory, applied examples, and practice /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Poznyak, Alexander S.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Diego : Elsevier, 2021.
Temas:
Mechanics.
Mechanics, Analytic.
Mechanics
M�ecanique.
M�ecanique analytique.
mechanics (physics)
Mechanics, Analytic
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Classical and Analytical Mechanics
  • Copyright
  • Contents
  • List of figures
  • List of tables
  • About the author
  • Preface
  • Notation
  • Introduction
  • 1 Kinematics of a point
  • 1.1 Products of vectors
  • 1.1.1 Internal (scalar) product
  • 1.1.2 Vector product
  • 1.1.3 Main properties of triple products
  • 1.2 Generalized coordinates
  • 1.2.1 Different possible coordinates
  • 1.2.2 Definition of generalized coordinates
  • 1.2.3 Relationship of generalized coordinates with Cartesian
  • 1.2.4 Coefficients of Lam�e
  • 1.3 Kinematics in generalized coordinates
  • 1.3.1 Velocity in generalized coordinates
  • 1.3.2 Acceleration in generalized coordinates
  • 1.4 Movement in the cylindrical and spherical coordinate systems
  • 1.4.1 Movement in cylindrical coordinates
  • 1.4.2 Movement in spherical coordinates
  • 1.5 Normal and tangential accelerations
  • 1.6 Some examples
  • 1.7 Exercises
  • 2 Rigid body kinematics
  • 2.1 Angular velocity
  • 2.1.1 Definition of a rigid body
  • 2.1.2 The Euler theorem
  • 2.1.3 Joint rotation with a common pivot
  • 2.1.4 Parallel and non-coplanar rotations
  • 2.2 Complex movements of the rigid body
  • 2.2.1 General relations
  • 2.2.2 Plane non-parallel motion and center of velocities
  • 2.3 Complex movement of a point
  • 2.3.1 Absolute velocity
  • 2.3.2 Absolute acceleration
  • 2.4 Examples
  • 2.5 Kinematics of a rigid body rotation
  • 2.5.1 Finite rotations
  • 2.5.2 Rotation matrix
  • 2.5.3 Composition of rotations
  • 2.6 Rotations and quaternions
  • 2.6.1 Quaternions
  • 2.6.2 Composition or summation of rotations as a quaternion
  • 2.7 Differential kinematic equations (DKEs)
  • 2.7.1 DKEs in Euler coordinates
  • 2.7.2 DKEs in quaternions: Poisson equation
  • 2.8 Exercises
  • 3 Dynamics
  • 3.1 Main dynamics characteristics
  • 3.1.1 System of material points
  • 3.1.2 Three main dynamics characteristics
  • 3.2 Axioms or Newton's laws
  • 3.2.1 Newton's axioms
  • 3.2.2 Expression for �Q
  • 3.2.3 Expression for �KA
  • 3.3 Force work and potential forces
  • 3.3.1 Elementary and total force work
  • 3.3.2 Potential forces
  • 3.3.3 Force power and expression for j
  • 3.3.4 Conservative systems
  • 3.4 Virial of a system
  • 3.4.1 Main definition of virial
  • 3.4.2 Virial for homogeneous potential energies
  • 3.5 Properties of the center of mass
  • 3.5.1 Dynamics of the center of inertia (mass)
  • 3.6 ``King/K�onig/Rey'' theorem
  • 3.6.1 Principle theorem
  • 3.6.2 Moment of inertia and the impulse moment with respect to a pivot
  • 3.6.3 A rigid flat body rotating in the same plane
  • 3.6.4 Calculation of moments of inertia for different rigid bodies
  • 3.6.5 K�onig theorem application
  • 3.6.6 Steiner's theorem on the inertia moment
  • 3.7 Movements with friction
  • 3.8 Exercises
  • 4 Non-inertial and variable-mass systems
  • 4.1 Non-inertial systems
  • 4.1.1 Newton's second law regarding a relative system

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