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ME
403
Intermediate Dynamics
Review of Newtonian Mechanics in plane motion, motion of rigid bodies in three dimensions, gyroscopic effects, principle of virtual work, D'Alembert's principle, Lagrange's equations of motion, case of impulsive forces, conservation laws, Lagrange's multipliers, variational calculus, Hamilton's principle, Hamilton's equations, Canonical transformations, The Hamilton-Jacobi equation.
Prerequisites:
0410211,0410240,0600203
0630403
(3-0-3)

Text Book:

Jerry Ginsberg, "Engineering Dynamics", Cambridge University Press, 2018.

Reference:

  • Donald Greenwood, "Advanced Dynamics", Cambridge University Press, 2003.  \
  • Haim Baruh, "Analytical Dynamics", McGraw-Hill, 1st Edition (October 23, 1998). \
  • L. Meirovitch, "Methods in Analytical Dynamics", Dover Publications, 2010.

Coordinator:

Dr. Abdullah Mohammed

Prerequisites by Topics:

  1. Newton's laws
  2. Kinematics of rigid bodies
  3. Energy methods
  4. Curvilinear integrals
  5. Differential equations

Objectives[^1]:

  1. Apply Newton's laws to the motion of rigid bodies in three dimensions. (1)
  2. Apply D\'Alembert's principle and Lagrange's equations for obtaining equations of motions of conservative and non-conservative systems, in the presence of holonomic and non-holonomic constraints. (1)
  3. Apply variational calculus and Hamilton's equations to obtain equations of motion of conservative and conservative systems (1)
  4. Apply the concept of canonical transformation to simplify Hamilton's equations. (1,7)

Topics:

  1. Review of vector analysis, coordinate frames
  2. Planar Newtonian Mechanics (Review)
  3. Motion of Rigid Bodies in Three Dimensions
  4. Gyroscopic Effects
  5. D\'Alembert's Principle
  6. Lagrange's Equations
  7. Hamilton's Equations (Canonical Transformations)

Evaluation Methods:

  1. Exams and Quizzes
  2. Homeworks
  3. Project

Learning Outcomes:

Objective 1

1.1 Students will be familiar with Euler's angles, and they will be able to determine the angular velocity vector for a rigid body in three-dimensional motion.

1.2 Students will be able to determine the inertia tensor and they will be able to determine the angular momentum and the kinetic energy of a rigid body in three-dimensional motion.

1.3 Students will be able to apply Newton's laws, the impulse and momentum method, and the work and energy method to a rigid body in three-dimensional motion.

Objective 2

2.1. Students will be familiar with the concept of virtual work and they will be able to write the equations of motion of a mechanical system using D\'Alembert's principle.

2.2 Students will be able to write Lagrange's equations of motion for conservative and nonconservative systems.

2.3 Students will be able to recognize the cyclic (ignorable) coordinates and to find the corresponding first integrals using Lagrange's equations.

2.4 Students will be able to apply Lagrange's multiplier method to systems with nonholonomic constraints and to give the physical meanings of the multipliers.

Objective 3

3.1 Students will be familiar with the use of variational calculus in solving physical problems and with its application to derive Lagrange's equations and Hamilton's equations.

3.2 Students will be able to write Hamilton's equations of motion of a mechanical system and to find the conservation laws from these equations.

Objective 4

4.1 Students will be able to define canonical transformations and their generating functions. They will be able to use such transformations to simplify Hamilton's equations of motion.

4.2 Students will be able to use canonical transformations in the derivation of Hamilton-Jacobi's equation of a mechanical system and to integrate the equation in the case of simple mechanical systems.

Course Classification

Student Outcomes Level Relevant Activities
1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. H Equations of motion, Solution of diff. Eqs., Integration, Multivariable Calculus, Lagrangian and Hamiltonian formulations of physical systems
2. An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. An ability to communicate effectively with a range of audiences.
4. An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. An ability to acquire and apply new knowledge as needed, using appropriate learning strategies. L Consultation to reference books

[^1]: Numbers in parentheses refer to the student outcomes