# Statics/Dynamics

Classical mechanics is a foundation of various mechanics topics such as strength of materials, fluid mechanics, machine design, mechanical vibrations, automatic control, finite elements, and so on. The concept of the moment of a force is introduced as static equilibrium requirements for rigid bodies. Then, dynamics is explained from kinematics arguments of motion to kinetics analysis of particles and rigid bodies. Various kinetic methods are explained through vector (Newtonian) methods, energy methods, and momentum methods.

Static Analysis

A static analysis calculates the effects of steady loading on a structure, while ignoring inertia and damping effects, such as those caused by time-varying loads. A static analysis can, however, include steady inertia loads (such as gravity and rotational velocity), and timevarying loads that can be approximated as static equivalent (wind and seismic loads commonly defined in many building codes) Static analysis is used to determine the displacements, stresses, strains, and forces in structures or components caused by loads that do not induce significant inertia and damping effects.

Dynamic Analysis

Dynamic analysis can be used to determine the vibration characteristics (natural frequencies and mode shapes) of a structure or a machine component while it is being designed. It also can be starting point for another, more detailed, dynamic analysis, such as a transient analysis, a harmonic analysis, or a spectrum analysis. Dynamic analysis is the study of the dynamic properties of structures under vibrational excitation.

Physical objects – Three common states of physical objects are gas, fluid, and solid. Thus, mechanics studies are often named by their medium, i.e. gas dynamics, fluid mechanics, and solid mechanics. Furthermore, mathematical idealization is adopted to consider physical objects as particles, or as either rigid or non-rigid deformable bodies.

Mechanical causes of motion – There are many mechanical causes of motion such as force, moment, work, impulse, and power, etc.

Mechanical responses – Two types of spatial motion for a physical object are translation and rotation. A general motion consists of these two motion components, which are independent of each other. This lays an important theoretical basis for rigid-body kinematics.

Cause and effect relationship – The governing physical laws are Newton’s three laws of motion and Euler’s equations. When Newton’s second law of motion is integrated, it becomes either the principle of work and energy or the principle of impulse and momentum. These laws are the foundations of all mechanics studies.

Newtons Law

I. Every body continues in its state of rest, or of uniform motion in a straight line, unless compelled to change its state by forces acting upon it (Law of inertia, N1L).

II. The time rate of change of linear momentum of a body is proportional to the force acting upon it and occurs in the direction in which the force acts (Law of motion, N2L).

III. To every action there is an equal and opposite reaction; that is, the mutual forces of two bodies acting upon each other are equal in magnitude, but opposite in direction (Law of action and reaction, N3L).

Free-Body Diagram

In solving a problem concerning the equilibrium of a rigid body, it is essential to consider all of the forces acting on the body. Therefore, the first step in determining the solution of a problem should be to draw a free-body diagram of the rigid body under consideration. Four steps are typically involved in drawing a free-body diagram: 1) isolating a body of interest, 2) indicating all the known applied forces, 3) indicating unknown reactive forces and moments due to supports and constraints, and 4) putting appropriate dimensions as needed.