Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler’s dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves.
1. Introduction - p. xxix 2. 1 Kinematics of a point - p. 1 3. 1.1: Products of vectors - p. 1 4. 1.2: Generalized coordinates - p. 8 5. 1.3: Kinematics in generalized coordinates - p. 10 6. 1.4: Movement in the cylindrical and spherical coordinate systems - p. 14 7. 1.5: Normal and tangential accelerations - p. 18 8. 1.6: Some examples - p. 20 9. 1.7: Exercises - p. 28 10. 2 Rigid body kinematics - p. 31 11. 2.1: Angular velocity - p. 31 12. 2.2: Complex movements of the rigid body - p. 38 13. 2.3: Complex movement of a point - p. 45 14. 2.4: Examples - p. 47 15. 2.5: Kinematics of a rigid body rotation - p. 59 16. 2.6: Rotations and quaternions - p. 71 17. 2.7: Differential kinematic equations (DKEs) - p. 84 18. 2.8: Exercises - p. 86 19. 3 Dynamics - p. 89 20. 3.1: Main dynamics characteristics - p. 90 21. 3.2: Axioms or Newton's laws - p. 91 22. 3.3: Force work and potential forces - p. 95 23. 3.4: Virial of a system - p. 100 24. 3.5: Properties of the center of mass - p. 103 25. 3.6: “King/König/Rey” theorem - p. 103 26. 3.7: Movements with friction - p. 123 27. 3.8: Exercises - p. 127 28. 4 Non-inertial and variable-mass systems - p. 131 29. 5 Euler's dynamic equations - p. 153 30. 6 Dynamic Lagrange equations - p. 189 31. 6.1: Mechanical connections - p. 189 32. 6.2: Generalized forces - p. 192 33. 6.3: Dynamic Lagrange equations - p. 195 34. 6.4: Normal form of Lagrange equations - p. 204 35. 6.5: Electrical and electromechanical models - p. 207 36. 6.6: Exercises - p. 217 37. 7 Equilibrium and stability - p. 221 38. 8 Oscillations analysis - p. 245 39. 8.1: Movements in the vicinity of equilibrium points - p. 245 40. 8.2: Oscillations in conservative systems - p. 249 41. 8.3: Several examples of oscillation analysis - p. 255 42. 8.4: Exercises - p. 270 43. 9 Linear systems of second order - p. 273 44. 9.1: Models governed by second order differential equations - p. 273 45. 9.2: Frequency response - p. 274 46. 9.3: Examples - p. 277 47. 9.4: Asymptotic stability - p. 286 48. 9.5: Polynomial robust stability - p. 303 49. 9.6: Exercises - p. 308 50. 10 Hamiltonian formalism - p. 311 51. 10.1: Hamiltonian function - p. 311 52. 10.2: Hamiltonian canonical form - p. 316 53. 10.3: First integrals - p. 321 54. 10.4: Some properties of first integrals - p. 323 55. 10.5: Exercises - p. 335 56. 11 The Hamilton–Jacobi equation - p. 337 57. 11.1: Canonical transformations - p. 337 58. 11.2: The Hamilton–Jacobi method - p. 339 59. 11.3: Hamiltonian action and its variation - p. 339 60. 11.4: Integral invariants - p. 343 61. 11.5: Canonicity criteria - p. 347 62. 11.6: The Hamilton–Jacobi equation - p. 361 63. 11.7: Complete integral of the Hamilton–Jacobi equation - p. 362 64. 11.8: On relations with optimal control - p. 369 65. 11.9: Exercises - p. 380 66. 12 Collection of electromechanical models - p. 383 67. 12.1: Cylindrical manipulator (2-PJ and 1-R) - p. 384 68. 12.2: Rectangular (Cartesian) robot manipulator - p. 387 69. 12.3: Scaffolding type robot manipulator - p. 389 70. 12.4: Spherical (polar) robot manipulator - p. 392 71. 12.5: Articulated robot manipulator 1 - p. 396 72. 12.6: Universal programmable manipulator - p. 399 73. 12.7: Cincinnati Milacron T3 manipulator - p. 404 74. 12.8: CD motor, gear, and load train - p. 412 75. 12.9: Stanford/JPL robot manipulator - p. 414 76. 12.10: Unimate 2000 manipulator - p. 418 77. 12.11: Robot manipulator with swivel base - p. 424 78. 12.12: Cylindrical robot with spring - p. 427 79. 12.13: Non-ordinary manipulator with shock absorber - p. 429 80. 12.14: Planar manipulator with two joints - p. 434 81. 12.15: Double “crank-turn” swivel manipulator - p. 437 82. 12.16: Robot manipulator of multicylinder type - p. 442 83. 12.17: Arm manipulator with springs - p. 445 84. 12.18: Articulated robot manipulator 2 - p. 459 85. 12.19: Maker 110 - p. 464 86. 12.20: Manipulator on a horizontal platform - p. 467 87. 12.21: Two-arm planar manipulator - p. 470 88. 12.22: Manipulator with three degrees of freedom - p. 476 89. 12.23: CD motor with load - p. 477 90. 12.24: Models of power converters with switching-mode power supply - p. 479 91. 12.25: Induction motor - p. 483 92. Bibliography - p. 487 93. Index - p. 489
Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler’s dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves.
1. Introduction - p. xxix 2. 1 Kinematics of a point - p. 1 3. 1.1: Products of vectors - p. 1 4. 1.2: Generalized coordinates - p. 8 5. 1.3: Kinematics in generalized coordinates - p. 10 6. 1.4: Movement in the cylindrical and spherical coordinate systems - p. 14 7. 1.5: Normal and tangential accelerations - p. 18 8. 1.6: Some examples - p. 20 9. 1.7: Exercises - p. 28 10. 2 Rigid body kinematics - p. 31 11. 2.1: Angular velocity - p. 31 12. 2.2: Complex movements of the rigid body - p. 38 13. 2.3: Complex movement of a point - p. 45 14. 2.4: Examples - p. 47 15. 2.5: Kinematics of a rigid body rotation - p. 59 16. 2.6: Rotations and quaternions - p. 71 17. 2.7: Differential kinematic equations (DKEs) - p. 84 18. 2.8: Exercises - p. 86 19. 3 Dynamics - p. 89 20. 3.1: Main dynamics characteristics - p. 90 21. 3.2: Axioms or Newton's laws - p. 91 22. 3.3: Force work and potential forces - p. 95 23. 3.4: Virial of a system - p. 100 24. 3.5: Properties of the center of mass - p. 103 25. 3.6: “King/König/Rey” theorem - p. 103 26. 3.7: Movements with friction - p. 123 27. 3.8: Exercises - p. 127 28. 4 Non-inertial and variable-mass systems - p. 131 29. 5 Euler's dynamic equations - p. 153 30. 6 Dynamic Lagrange equations - p. 189 31. 6.1: Mechanical connections - p. 189 32. 6.2: Generalized forces - p. 192 33. 6.3: Dynamic Lagrange equations - p. 195 34. 6.4: Normal form of Lagrange equations - p. 204 35. 6.5: Electrical and electromechanical models - p. 207 36. 6.6: Exercises - p. 217 37. 7 Equilibrium and stability - p. 221 38. 8 Oscillations analysis - p. 245 39. 8.1: Movements in the vicinity of equilibrium points - p. 245 40. 8.2: Oscillations in conservative systems - p. 249 41. 8.3: Several examples of oscillation analysis - p. 255 42. 8.4: Exercises - p. 270 43. 9 Linear systems of second order - p. 273 44. 9.1: Models governed by second order differential equations - p. 273 45. 9.2: Frequency response - p. 274 46. 9.3: Examples - p. 277 47. 9.4: Asymptotic stability - p. 286 48. 9.5: Polynomial robust stability - p. 303 49. 9.6: Exercises - p. 308 50. 10 Hamiltonian formalism - p. 311 51. 10.1: Hamiltonian function - p. 311 52. 10.2: Hamiltonian canonical form - p. 316 53. 10.3: First integrals - p. 321 54. 10.4: Some properties of first integrals - p. 323 55. 10.5: Exercises - p. 335 56. 11 The Hamilton–Jacobi equation - p. 337 57. 11.1: Canonical transformations - p. 337 58. 11.2: The Hamilton–Jacobi method - p. 339 59. 11.3: Hamiltonian action and its variation - p. 339 60. 11.4: Integral invariants - p. 343 61. 11.5: Canonicity criteria - p. 347 62. 11.6: The Hamilton–Jacobi equation - p. 361 63. 11.7: Complete integral of the Hamilton–Jacobi equation - p. 362 64. 11.8: On relations with optimal control - p. 369 65. 11.9: Exercises - p. 380 66. 12 Collection of electromechanical models - p. 383 67. 12.1: Cylindrical manipulator (2-PJ and 1-R) - p. 384 68. 12.2: Rectangular (Cartesian) robot manipulator - p. 387 69. 12.3: Scaffolding type robot manipulator - p. 389 70. 12.4: Spherical (polar) robot manipulator - p. 392 71. 12.5: Articulated robot manipulator 1 - p. 396 72. 12.6: Universal programmable manipulator - p. 399 73. 12.7: Cincinnati Milacron T3 manipulator - p. 404 74. 12.8: CD motor, gear, and load train - p. 412 75. 12.9: Stanford/JPL robot manipulator - p. 414 76. 12.10: Unimate 2000 manipulator - p. 418 77. 12.11: Robot manipulator with swivel base - p. 424 78. 12.12: Cylindrical robot with spring - p. 427 79. 12.13: Non-ordinary manipulator with shock absorber - p. 429 80. 12.14: Planar manipulator with two joints - p. 434 81. 12.15: Double “crank-turn” swivel manipulator - p. 437 82. 12.16: Robot manipulator of multicylinder type - p. 442 83. 12.17: Arm manipulator with springs - p. 445 84. 12.18: Articulated robot manipulator 2 - p. 459 85. 12.19: Maker 110 - p. 464 86. 12.20: Manipulator on a horizontal platform - p. 467 87. 12.21: Two-arm planar manipulator - p. 470 88. 12.22: Manipulator with three degrees of freedom - p. 476 89. 12.23: CD motor with load - p. 477 90. 12.24: Models of power converters with switching-mode power supply - p. 479 91. 12.25: Induction motor - p. 483 92. Bibliography - p. 487 93. Index - p. 489
