By Murray S. Klamkin

Designed for lecture room use, this ebook includes brief, self-contained mathematical types of difficulties within the actual, mathematical, and organic sciences first released within the lecture room Notes part of the SIAM evaluate from 1975-1985. the issues supply an effective way to make advanced material extra obtainable to the scholar by utilizing concrete purposes. each one part has wide supplementary references supplied via the editor from his years of expertise with mathematical modelling.

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**Example text**

The path of the rear wheels is found by piecing together solutions from the two special cases above (see Figure 2b). Normally in making a right turn (left turn in Britain) r < L. Hence when the turn is initiated too close to the corner, a rear wheel will go over the curb (a common experience for bus riders). ii) Changing lanes. Changing lanes or pulling out from a curb can be modelled by having the point given by P traverse an eighth of a circle followed by another eighth of a circle in the opposite direction so as to "straighten" out the front wheels (see Fig.

The necessity of the unknown scalar factor y(t) is what makes this problem interesting. The solution of (1) is Integrating by parts and setting p,(0) = />/i0, / = 1, 2, we obtain Let £(0 = exp (/0' 7(5) ds). ,,0 + fof(s)p'\(s) ds, so that q'(t) = £ ( t ) p \ ( t ) . ;(/), (4) becomes Unfortunately, we are unable to explicitly solve this equation. We are able to get a simple differential equation for £(/) when the motion of the front of the bus is described as a solution of the second order linear differential equation, where a, b, c are constant and d = (*/,, d2) is a fixed vector.

The authors are indebted to Mr. Walter Aiello for providing computer drawn figures. REFERENCES [ 1 ] JOHN BAYLIS, The mathematics of a driving hazard, Math. , 57 (1973), pp. 23-26. [2] EDWARD A. , 21 (1979), pp. 136-138. ICE BREAKING WITH AN AIR CUSHION VEHICLE* E. R. MULLERt Abstract. The ice breaking mechanism under a slow moving air cushion vehicle is explored. The bending moments which cause the circumferential cracks in the ice are determined for the case where the pressure of the air cushion is sufficient to depress the water and force air below the ice field.