Introduction to Dynamics

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Introduction to Dynamics

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DYNAMICS: PART OF RIGID BODY MECHANICS  In Chapter 1 of the book we had defined Mechanics as that branch of physical science which is concerned with the resultant effect of forces on bodies, both in a state of rest or in motion. Mechanics is subdivided into three branches viz. Mechanics of Rigid Bodies, Mechanics of Deformable Bodies and Mechanics of Fluids.  Mechanics of Rigid Bodies is the branch of Mechanics where the body is assumed to be perfectly rigid i.e there is no relative movement between the particles forming the body and also there is no deformation of the body under the action of the forces. Though engineering structures and machines do have slight deformation under the action of loads, still they are treated as rigid bodies since the deformations are very small and they can be neglected. We can thus apply the conditions of equilibrium to such static bodies and the equations of motions to moving bodies.  Mechanics of Rigid Bodies is further divided into Statics and Dynamics.

Statics is that part of Rigid Body Mechanics which analysis bodies at rest.

On the other hand, Dynamics is that part of Rigid Body Mechanics which analyses motion of moving bodies. By the application of motion analysis we wish to gather information about the following parameters of a moving body.

1) the path traced by moving body 2) the rate at which the body moves 3) the time aspect of motion 4) the position occupied by the body during motion 5) the forces acting on the body which are responsible for the motion 6) the relation between the forces and the motion so produced

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The study of Dynamics herein would help us in answering all the above questions about a moving body.

KINEMATICS AND KINETICS  Dynamics is further subdivided into Kinematics and Kinetics. Bodies acquire motion due to the action of forces on it. The Kinematics part of Dynamics is concerned only with the study of motion of the body without consideration of the forces which have caused the motion of the body.

Kinematics therefore analyses only the geometry of the motion.  Kinetics is that part of Dynamics which relates the forces acting on the body to the motion of the body. By knowing the forces acting on the body we can predict the resultant motion of the body using the various laws and principles of Kinetics.

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PARTICLE DYNAMICS  The motion analysis of a body is referred to as Particle Dynamics when the body is idealized as a particle.  Particle Dynamics may be Kinematic Analysis or could be Kinetic Analysis of motion. When we idealise a body as a particle it does not mean that we are dealing with minute point like object. It rather means that the size and shape of the body is of no consequence in the analysis of the motion.  For example if we wish to analyse the motion of a ship traveling between two ports, kilometers apart, then the shape and size of the ship is of no relevance in Motion Analysis. Hence motion of the

ship can be

characterized by motion of its mass centre. Whenever a body is treated as a particle, all the forces acting on the body are assumed to be concurrent at the mass centre of the body.  Any rotation of the body is also neglected. For example if we analyse the motion of an airplane, treating it as a particle is justifiable, as long as we are interested to know the position, rate of motion or the path described by an airplane.  However if the plane experiences turbulent motion due to low air pressure pocket then the motion analysis at such an instant cannot be carried out treating the airplane as a particle. In such situations Rigid Body Dynamics has an important role to play.

RIGID BODY DYNAMICS  In Rigid Body Dynamics, motion analysis involves the shape and size of the body. Since the size is involved, the forces, usually of non-concurrent type act at different locations on the body and they tend to cause rotation of the body apart from moving the body. The relation between the forces and the motion so produced is studied in Kinetic Analysis of Rigid Bodies. The relations between the motions of different particles forming the rigid body are studied in Kinematics of Rigid Bodies.  In this book, the Particle Dynamics has been dealt in Chapters 9, 10, 11 and 12. Chapter 9 involves Kinematics of Particles whereas Chapters 10, 11 and 12 deal with Kinetics of Particles.  Kinematics of Rigid Body Dynamics is dealt with in Chapters 13. Kinetics of rigid Bodies is not dealt with us it is beyond the scope of this book.

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REFERENCE FRAME  For any motion analysis, we need to take a reference frame i.e an origin with a set of co-ordinate axes, for measurement of motion parameters. The reference frame could be fixed or moving.  Newtonian frame of reference also known as inertial reference frame is a set of co-ordinates axes fixed or moving with uniform velocity. Newton's laws are valid for such a reference frame.  For most of our engineering applications, the Newtonian reference frame is fixed at the earth, assuming it to be stationary. This assumption will not introduce any significant error in the calculations, since earth's angular velocity or angular acceleration is very small as compared to the moving bodies on which we work However for motion analysis of planets, satellites or rockets, we are required to fix the Newtonian reference frame on a fixed star like the Sun.

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EXERCISE Theory Questions Q. 1. List any ten applications where knowledge of Dynamics would be essential.

Q. 2. What are different branches of dynamics? Explain with suitable examples.

Q. 3. What is meant by motion analysis? Explain with an illustration.

Q. 4. Explain kinematic and kinetics with suitable example.

Q. 5. When is the motion analysis referred to as Particle. Dynamics and when as Rigid Body Dynamics.

Q. 6. Write a short note on "Newtonian reference frame".

UNIVERSITY QUESTIONS 1. Find out forces in FB and BE using method of section and other by method of joints.

members (8 Marks)

AF = FB = FE = ED = 2m CE = 3m 2. Determine the Centre of gravity of the shaded area.

(8 Marks)

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3. A particle moves in a straight line with a velocity-time diagram shown in figure. If S=-25m at t=0, draw displacement – time and acceleration time diagrams for 0 to 24 seconds.

(6 Marks)

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