Mathematics of Physics and Engineering
46 Kinematics and Dynamics of a Point Mass to study the motion of bodies under Earth's gravity. Even though many modern historia ...
Parallel Translation of Frames 47 starting point is the analysis of the relative motion of frames. The easiest motion is paralle ...
(^48) Kinematics and Dynamics of a Point Mass As an EXAMPLE, consider a golf ball in a moving elevator. We fix the frame O on th ...
Uniform Rotation of Frames 49 path r(t) — votr of the point mass relative to the car is a straight line, since there is no angul ...
50 Kinematics and Dynamics of a Point Mass the design of water-wheels. More familiar effects of the Coriolis force, such as rota ...
Uniform Rotation of Frames 51 circle of radius R with uniform angular velocity u (Figure 2.1.4). Denote by r(t) the position vec ...
52 Kinematics and Dynamics of a Point Mass on page 62. Let the frame 0\ rotate relative to the frame O so that the corresponding ...
Uniform Rotation of Frames 53 2u> x ri, and the centripetal acceleration o,c — u} x [u) x fi). Note that o,c is orthogonal to ...
54 Kinematics and Dynamics of a Point Mass (1.3.27), page 36, we find ag = 0 and so rl=ar = -j^2 Rr, (2.1.25) where R is the rad ...
Uniform Rotation of Frames 55 Newton's Second Law implies mr = F. By (2.1.24), mf\ = F - 2mu> xfi- mu> x (u> x n). (2.1 ...
56 Kinematics and Dynamics of a Point Mass of both frames are at the Earth center. Suppose that a point mass m is in the Norther ...
Uniform Rotation of Frames 57 Direction of Motion North South East West Deflection of trajectory East West South North For moti ...
58 Kinematics and Dynamics of a Point Mass dulum starts to swing in the Northern Hemisphere in the meridian plane, then the Cori ...
Uniform Rotation of Frames 59 speeds stay the same throughout the revolution of the swing plane, then the weight will be rotatin ...
60 Kinematics and Dynamics of a Point Mass 60° /• / Polar Easterlies / / //y'Temperate Westerlies/ / 30°/ Calms of Cancer // Eas ...
General Accelerating Frames 61 EXERCISE 2.1.14. Explain the formation of the temperate westerlies and the polar easterlies. EXER ...
(^62) Kinematics and Dynamics of a Point Mass Fig. 2.1.9 3-D Rotation of Frames Similarly, we take the dot product of both sides ...
General Accelerating Frames^63 that the matrix UT is a representation, in the basis (z, j, k), of an or- thogonal transformation ...
(^64) Kinematics and Dynamics of a Point Mass Hint: direct computation, (h) Consider the vector OP = ro(i) = x(t) i + y(t)j + z( ...
General Accelerating Frames 65 the equality ro(t) = U{t)r{t), where f{t) = x(t)i + y{t) j + z{t) k. Also keep in mind that, desp ...
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