Dr. Wang Xingbo Email: xbwang.nudt@gmail QQ:168731668 Homepage: wxbstudio.home4u.china

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Dr. Wang XingboDr. Wang XingboEmail: xbwang.nudt@gmail.comEmail: xbwang.nudt@gmail.com

QQ:168731668QQ:168731668Homepage: wxbstudio.home4u.china.comHomepage: wxbstudio.home4u.china.com

FallFall ，， 20052005

Mathematical & MechanicalMathematical & MechanicalMethod in Mechanical EngineeringMethod in Mechanical Engineering

1.1. Mechanical Engineering is being a subject of Mechanical Engineering is being a subject of sciencescience

2.2. Development of cross &Multi-subjects,especially Development of cross &Multi-subjects,especially Computer science

3.3. Future requirements of persons in research Future requirements of persons in research workwork

Motivation of This CourseMotivation of This Course

1.1. To show idea of scientific methodologyTo show idea of scientific methodology

2.2. To introduce fundamental methodsTo introduce fundamental methods

3.3. To agitate the creative competenceTo agitate the creative competence

4.4. To dig out one or more elitesTo dig out one or more elites

Purpose of the coursePurpose of the course

1.1. Experiential Method Experiential Method

2.2. Scientific Method Scientific Method

Methodology Methodology

Originates from people’s experience and Originates from people’s experience and intuition without any logical or scientific intuition without any logical or scientific principlesprinciples

Methodology Methodology Experiential MethodExperiential Method

1. Utility 1. Utility

2. Simple 2. Simple

3. 3. Trial Trial

Experiential Method Experiential Method --TraitsTraits

1.1. A method but not the perfect oneA method but not the perfect one

2.2. Less cost but high efficientLess cost but high efficient

3.3. Without extension Without extension

Experiential MethodExperiential Method - -EvaluationEvaluation

A process by which scientists, collectivelA process by which scientists, collectively and over-time, endeavor to construct ay and over-time, endeavor to construct an accurate representation of the worldn accurate representation of the world

Scientific Method Scientific Method

1. Observation and description

2. Formulation of a hypothesis

3. Use of the hypothesis

4. Performance of experimental tests

Scientific Method-Scientific Method-Four StepsFour 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

Scientific Method:Scientific Method:Hypotheses, Models, Theories and Laws 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

Scientific Method:Scientific Method:Solving Problems with Scientific Methods 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 Models 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 Models Mathematical Models

1. Newtonian Dynamics

2. LaGrangian and Hamiltonian Dynamics

Mechanical Models 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 force

s have equal magnitudes and opposite directions.

Mechanical Models :Mechanical Models :Newtonian Dynamics

The actual path of a dynamical system in configuration space extermeizes the action between two defined locations and times

Mechanical Models :Mechanical Models :LaGrangian and Hamiltonian Dynamics

Chapter 1: Scientific methodsChapter 2 and 3: Vector and tensorChapter 4: Differential form Chapter5: Variational calculusChapter 6: Lie groupChapter 7: Manifold theoryChapter 8: Classical mechanics Chapter 9 :Finite deformation

Contents in this course Contents in this course

Course procedure:20%

Homework & Discussion:20%

Final Exam:60%

About ExaminationAbout Examination

Chapter 1 is over!

Take a rest!

To be continued……

11:00am.,Oct.,26,200511:00am.,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 Models:Mathematical Models:Building a Mathematical Model 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 Models:Mathematical Models:Verifying and Refining a Model Verifying and Refining a Model

1. Output variables

2. Input variables

3. Parameters (constants)

Mathematical Models:Mathematical Models:Variables and Parameters 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 Models:Mathematical Models:Continuous /Discrete in Time

Dr. Wang Xingbo Email: xbwang.nudt@gmail QQ:168731668 Homepage: wxbstudio.home4u.china

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