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By Walter Greiner

The sequence of texts on Classical Theoretical Physics is predicated at the hugely profitable sequence of classes given through Walter Greiner on the Johann Wolfgang Goethe college in Frankfurt am major, Germany. meant for complicated undergraduates and starting graduate scholars, the volumes within the sequence offer not just a whole survey of classical theoretical physics but in addition an important variety of labored examples and difficulties to teach scholars truly how one can observe the summary rules to lifelike difficulties.

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Example text

What is the equation of the straight line through A and B? Solution A (b -a ) The straight line AB is parallel to (b − a). Moreover, it passes through point A. Hence, the equation determining any position vector x of a point X on the desired straight line reads a b x = a + t (b − a), B X x x with t being a real number (running parameter −∞ < t < ∞). The point-direction form of a straight If two points A and B are not given but one point A and a vector line. u specifying the orientation of the straight line are given, the equation of the straight line reads x = a + tu .

One has |v| = R 2 ω2 + b2 ω2 = ω R 2 + b2 , that is, the magnitude of the velocity is constant. The acceleration is the derivative of the velocity b = −ω2 · (R cos ωt, R sin ωt, 0) = −ω2 r⊥ , where r⊥ = (R cos ωt, R sin ωt, 0) = (r · er )er and er = (cos ωt, sin ωt, 0) is the polar unit vector in the x, y-plane. We thus obtain the same acceleration as for the circular motion. For the magnitude, it holds that |b| = ω2 R. Integration of vectors: The integration rules may be applied also to vectors in the customary way.

A strong breeze blows from the west with 120 km/h relative to ground. What are the velocity and direction of flight of the plane, assuming that there is no wind deflection? y w vm vo ϕ West North 45º ey ex x East South The relative directions of wind and airplane velocity. Solution Let |vm | = 930 km/h, the velocity of the plane in the wind, |v0 | = the velocity of the plane without wind, |w| = the wind velocity. 2◦ . 12 COMPONENT REPRESENTATION OF A VECTOR r = xi + yj + zk, |r| = P(x,y,z) or: r = (x, y, z); r= z = x 2+ y 2+ z2 (x , y,z ) y |r| The position vector: A point P in space may be z uniquely fixed by specifying the vector beginning at the origin of the coordinate frame and pointing to the point P as endpoint.

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