Dynamics ديناميكا (رقم المادة: 804222) محاضرات الدكتور: حسن عبدالإله علي فدعق الفصل الدراسي الثاني لعام: 1427/1428 هـ

Lecture I Introduction

Talking Points What is dynamics? Historical background Why do we need to study dynamics Subject outline Some relevant concepts Units

What is Dynamics?

What is Dynamics? (Cont.)

Historical Background Galileo (1564-1642): Bodies in free fall, motion on inclined plane, and motion of the pendulum

Historical Background (Cont.) Newton (1642-1727) Laws of motion, law of universal gravitation (F = ma) Euler, D’Alembert, Lagrange, Laplace, Coriolis, Einstein,etc.

Why do we need to study dynamics Dynamics principles are basic to the analysis and design of moving structures, such as, engine parts (cams, pistons, gears, etc.), air crafts, missiles, rockets, automatic control systems, turbines, pumps, machine tools, etc.

Why do we need to study dynamics (Cont.) How do we decide how big to make the pistons? Where should they be placed in the engine block? How do we make the engine run smoothly? Well, we could answer these questions by trial and error. But the 'errors' would be expensive exercises. Why not study the dynamics of engines and make some predictions instead?

Why do we need to study dynamics (Cont.) Or suppose we want to build a robot. How do we decide how big to make the motors? How fast can we expect it to move from one place to another? How accurate will it be while it moves and stops? How many joints should it have and where?

Subject Outline

Kinematics of Particles Rectilinear Motion Curvilinear Motion

Kinematics of Particles Relative Motion Constrained Motion vA vB vB/A

Coordinates Used for Curvilinear Motion Normal-Tangential coordinates Polar coordinates Rectangular coordinates

Kinematics of Rigid Bodies

Kinetics of Particles

Some Relevant Concepts Particle: A body of negligible dimensions (or when its dimensions are irrelevant to the description of its motion or the action of the forces on it). Bodies of finite size, such as rockets, projectiles, or vehicles. Rigid Body: A system of particles for which the distances between the particles remain unchanged when it moves. It is a body whose changes in shape are negligible compared with the overall dimensions of the body or with the changes in position of the body as a whole. Constrained Motion: When a body is confined to move along a certain path. Unconstrained Motion: When a body has no physical guides to move in and it follows a path determined by its initial motion and by the forces applied to it.

Some Relevant Concepts (Cont.) Newton’s Laws: Law I: A body remains at rest or continues to move with uniform velocity if there is no unbalanced force acting on it. Law II: The acceleration of a body is proportional to the resultant force acting on it and is in the direction of this force (F = ma). Law III: The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

Units & Notation Vector Scalar or Conversion Form US to SI US Unit SI Unit Symbol Quantity 1 slug = 14.594 kg slug kg m Mass 1 ft = 0.3048 m ft l Length ------ sec s t Time 1 lb = 4.4482 N lb N f Force Gravitational acceleration (g) = 9.81 m/s2 = 32.2 ft/s2 Vector Scalar or