Dr. Wang Xingbo QQ: Homepage: wxbstudio.home4u.china.com Fall ， 2005 Mathematical & Mechanical Method in Mechanical Engineering

1.Mechanical Engineering is being a subject of science 2.Development of cross &Multi-subjects,especially Computer science Computer science Computer science 3.Future requirements of persons in research work Mathematical & Mechanical Method in Mechanical Engineering Motivation of This Course

1. To show idea of scientific methodology 2. To introduce fundamental methods 3. To agitate the creative competence 4. To dig out one or more elites Mathematical & Mechanical Method in Mechanical Engineering Purpose of the course

1.Experiential Method 2.Scientific Method Mathematical & Mechanical Method in Mechanical Engineering Methodology

Originates from people’s experience and intuition without any logical or scientific principles Mathematical & Mechanical Method in Mechanical Engineering Methodology Experiential Method

1. Utility 2. Simple 3. Trial Mathematical & Mechanical Method in Mechanical Engineering Experiential Method -Traits

1.A method but not the perfect one 2.Less cost but high efficient 3.Without extension Mathematical & Mechanical Method in Mechanical Engineering Experiential Method -Evaluation

A process by which scientists, collectively and over-time, endeavor to construct an accurate representation of the world Mathematical & Mechanical Method in Mechanical Engineering Scientific Method

1.Observation and description 2.Formulation of a hypothesis 3.Use of the hypothesis 4. P erformance of experimental tests Mathematical & Mechanical Method in Mechanical Engineering Scientific Method-Four Steps

1.A hypothesis is a limited statement regarding cause and effect in specific situations 2. A model is reserved when hypothesis has is valid 3.A scientific theory or law represents a hypothesis confirmed through repeated experimental tests Mathematical & Mechanical Method in Mechanical Engineering Scientific Method: Hypotheses, Models, Theories and Laws

Step1. State the problem Step 2. Research the problem Step 3. Form a hypothesis Step 4. Test the hypothesis Step 5. Draw conclusions from the data Mathematical & Mechanical Method in Mechanical Engineering Scientific Method: Solving Problems with Scientific Methods

A process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models Four procedures as follows

    1.Building a Mathematical Model        2.Verifying and Refining a Model        3.Variables and Parameters     4.Continuous /Discrete in Time Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models

1.Newtonian Dynamics 2.LaGrangian and Hamiltonian Dynamics Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models

1.A body remains at rest or in a uniform state of motion if no external force acts on it. 2. A body, upon which a force acts, moves in such a way that the time rate of change of the momentum equals the force. 3. If two bodies act on one another by means of forces, these forces have equal magnitudes and opposite directions. Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models : Newtonian Dynamics

The actual path of a dynamical system in configuration space extermeizes the action between two defined locations and times Mathematical & Mechanical Method in Mechanical Engineering Mechanical Models : LaGrangian and Hamiltonian Dynamics

Chapter 1: Scientific methods Chapter 2 and 3: Vector and tensor Chapter 4: Differential form Chapter5: Variational calculus Chapter 6: Lie group Chapter 7: Manifold theory Chapter 8: Classical mechanics Chapter 9 :Finite deformation Mathematical & Mechanical Method in Mechanical Engineering Contents in this course

Course procedure:20% Homework & Discussion:20% Final Exam:60% Mathematical & Mechanical Method in Mechanical Engineering About Examination

Chapter 1 is over! Take a rest! To be continued…… Mathematical & Mechanical Method in Mechanical Engineering 11:00am.,Oct.,26,2005

1.Identify the problem 2.Begin with a simple model. 3.Identify important variables and constants. 4.Develop the equation(s) Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Building a Mathematical Model

1.Is the information produced reasonable? 2.Are the assumptions made? 3.Are there any factors not considered? 4.How do the results, if available? Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Verifying and Refining a Model

1.Output variables 2.Input variables 3.Parameters (constants) Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Variables and Parameters

1.Is the information produced reasonable? 2.Are the assumptions made? 3.Are there any factors not considered? 4.How do the results, if available? Mathematical & Mechanical Method in Mechanical Engineering Mathematical Models: Continuous /Discrete in Time