[数学]美国数学建模写作培训.ppt

c. represents the final kinetic energy of a cycle, as well as the of the next cycle. Considering that the snowboarder experiences more than one cycle, it is not wise to chase a higher jump at the cost of less . The situations are similar for the width, the height and the flat. The wider course, the larger height and the longer flat result in large vertical air while less . Therefore, the half-pipe should not be too wide, too high or too flat. Validity Using recommended width, height, flat length and gradient angle, with other parameters, the resulting maximum Vertical Air is about 7 meters. This result matches the Shaun White’s best performance and is consistent with The common “Vertical Air” (12 feet~20 feet for men and 6 feet~15 feet for women) in Snowboard half-pipe games. Sensitivity As to the sensitivity, we modified parameters by ±10%, and the result supports that the numerical simulation is robust. Complement In the basic model above, we neglect the influence of the snowboarder on the flying path, but rather pay most attention to the objective factors. Nevertheless, snowboarder is the key role in this sport. Now we take the impact of the snowboarder into account. The direction of velocity A snowboarder is different from an rigid body in that he can turn, decelerate etc. where a small ball or a stick can’t. A skilled snowboarder may move in a direction partly determined by himself. This is why we discussed how to choose the ‘best path’ in a given course. The larger is, the longer flying distance is. As a result, the cycle distance would be longer, which results in fewer cycles. However, since a snowboarder must perform 5 to 8 acrobatic tricks in the Winter Olympic Games, fewer cycles are not allowed. Hence, a snowboarder should avoid flying too far. At the same time, however, a larger means greater wh