variables1

# variables1 - Variable Definition Notes comments Extended...

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1 Variable Definition Notes & comments Pi-theorem (also definition of physical quantities,…) Physical similarity means that Physical similarity all Pi-parameters are equal Galileo-number (solid mechanics) Reynolds number (fluid mechanics) Extended base dimension system Lectures 1-3 and PS2 Important concepts include the extended base dimension system, distinction between units and dimensions, the formal Pi-theorem based procedure and the concept of physical similarity. Applications include calculation of physical processes like atomic explosion, drag force on buildings etc.

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2 Variable Definition Notes & comments r v v r = dx r / dt Velocity vector r r a a = dv r / dt Acceleration vector Unit vectors that e r r r 1 , e 2 , e 3 define coordinate system = basis Normal vector r Always points outwards of n domain considered Force vector (force that acts on a material point) Angular momentum r x x r = x e r + x r r 1 1 2 e 2 + x 3 e 3 Position vector r r r p p = mv = m ( v 1 e r 1 + v 2 e r v e r 2 + 3 3 ) Linear momentum x r r r r r r i × p i x i × p i = x i × m i v i r F F r = F e r r r x x + F y e y + F z e z Covered in lecture 4 and PS1 Basic definitions of linear momentum, angular momentum, normal vector of domain boundaries
3 Variable Definition Notes & comments Dynamic resultant theorem r v def r Change of linear momentum d ( p ) / dt = d ( mv ) / dt = F is equal to sum of external forces Dynamic moment theorem Change of the angular motion of a discrete system of i = 1,N particles is equal to the sum of the moments (or torque) generated by external forces Newton’s three laws Static EQ (solve truss problems) 1. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. 2. The change of motion is proportional to the motive force impresses, and is made in the direction of the right line in which that force is impressed. 3. To every action there is always opposed an equal reaction: or, the mutual action of two bodies upon each other are always equal, and directed to contrary parts.

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## This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

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variables1 - Variable Definition Notes comments Extended...

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