2022小美赛A题How Pterosaurs Fly翼龙是如何飞行的思路分享

简介: 2022小美赛A题How Pterosaurs Fly翼龙是如何飞行的思路分享

2022小美赛A题How Pterosaurs Fly翼龙是如何飞行的思路分享

点击链接【2022小美赛数学建模思路分享】:https://jq.qq.com/?_wv=1027&k=pYYvA9gJ

点击链接【2022小美赛数学建模思路分享】:https://jq.qq.com/?_wv=1027&k=pYYvA9gJ

点击链接【2022小美赛数学建模思思路分享】:https://jq.qq.com/?_wv=1027&k=pYYvA9gJ

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2022小美赛翻译A题How Pterosaurs Fly思路分享

点击链接加入群聊【2022小美赛数学建模思】:https://jq.qq.com/?_wv=1027&k=pYYvA9gJ

Pterosaurs is an extinct clade of flflying reptiles in the order, Pterosauria. They

existed during most of the Mesozoic: from the Late Triassic to the end of

the Cretaceous. Pterosaurs are the earliest vertebrates known to have evolved

powered flflight. Their wings were formed by a membrane of skin, muscle, and

other tissues stretching from the ankles to a dramatically lengthened fourth

fifinger[1].

There were two major types of pterosaurs. Basal pterosaurs were smaller

animals with fully toothed jaws and long tails usually. Their wide wing mem

branes probably included and connected the hind legs. On the ground, they

would have had an awkward sprawling posture, but their joint anatomy and

strong claws would have made them effffective climbers, and they may have lived

in trees. Basal pterosaurs were insectivores or predators of small vertebrates.

Later pterosaurs (pterodactyloids) evolved many sizes, shapes, and lifestyles.

Pterodactyloids had narrower wings with free hind limbs, highly reduced tails,

and long necks with large heads. On the ground, pterodactyloids walked well on

all four limbs with an upright posture, standing plantigrade on the hind feet and

folding the wing fifinger upward to walk on the three-fifingered “hand”. The fossil

trackways show at least some species were able to run and wade or swim[2].

Pterosaurs sported coats of hair-like fifilaments known as pycnofifibers, which

covered their bodies and parts of their wings[3]. In life, pterosaurs would have

had smooth or flfluffffy coats that did not resemble bird feathers. Earlier sug

gestions were that pterosaurs were largely cold-blooded gliding animals, de

riving warmth from the environment like modern lizards, rather than burning

calories. However, later studies have shown that they may be warm-blooded

(endothermic), active animals. The respiratory system had effiffifficient unidirec

tional “flflow-through” breathing using air sacs, which hollowed out their bones

to an extreme extent. Pterosaurs spanned a wide range of adult sizes, from

the very small anurognathids to the largest known flflying creatures, including

Quetzalcoatlus and Hatzegopteryx4, which reached wingspans of at least

nine metres. The combination of endothermy, a good oxygen supply and strong

1muscles made pterosaurs powerful and capable flflyers.

The mechanics of pterosaur flflight are not completely understood or modeled

at this time. Katsufumi Sato did calculations using modern birds and concluded

that it was impossible for a pterosaur to stay aloft[6]. In the book Posture,

Locomotion, and Paleoecology of Pterosaurs it is theorized that they were able

to flfly due to the oxygen-rich, dense atmosphere of the Late Cretaceous period[7].

However, both Sato and the authors of Posture, Locomotion, and Paleoecology

of Pterosaurs based their research on the now-outdated theories of pterosaurs

being seabird-like, and the size limit does not apply to terrestrial pterosaurs,

such as azhdarchids and tapejarids. Furthermore, Darren Naish concluded that

atmospheric difffferences between the present and the Mesozoic were not needed

for the giant size of pterosaurs[8].

Another issue that has been diffiffifficult to understand is how they took offff.

If pterosaurs were cold-blooded animals, it was unclear how the larger ones

of enormous size, with an ineffiffifficient cold-blooded metabolism, could manage

a bird-like takeoffff strategy, using only the hind limbs to generate thrust for

getting airborne. Later research shows them instead as being warm-blooded

and having powerful flflight muscles, and using the flflight muscles for walking as

quadrupeds[9]. Mark Witton of the University of Portsmouth and Mike Habib of

Johns Hopkins University suggested that pterosaurs used a vaulting mechanism

to obtain flflight[10]. The tremendous power of their winged forelimbs would

enable them to take offff with ease[9]. Once aloft, pterosaurs could reach speeds

of up to 120 km/h and travel thousands of kilometres[10].

Your team are asked to develop a reasonable mathematical model of the

flflight process of at least one large pterosaur based on fossil measurements and

to answer the following questions.

\1. For your selected pterosaur species, estimate its average speed during nor

mal flflight.

\2. For your selected pterosaur species, estimate its wing-flflap frequency during

normal flflight.

\3. Study how large pterosaurs take offff; is it possible for them to take offff like

birds on flflat ground or on water? Explain the reasons quantitatively.

翼龙是一种已灭绝的飞行爬行动物分支。它们存在于中生代的大部分时间:从晚三

叠纪到白垩纪末期。翼龙是已知的最早进化出动力飞行的脊椎动物。它们的翅膀是

由皮肤、肌肉和其他组织组成的膜,从脚踝延伸到一个显著延长的第四指[1]。

翼龙主要有两种类型。基底翼龙是一种体型较小的动物,通常有全齿的下颚和

长长的尾巴。它们的宽翼膜可能包括并连接了后腿。在地面上,它们可能会有一个

笨拙的伸展姿势,但它们的关节解剖结构和强壮的爪子会使它们成为有效的攀登者

,而且它们可能生活在树上。基底翼龙是食虫动物或小型脊椎动物的捕食者。后来

,翼龙(翼手龙)进化出了许多体型、形状和生活方式。翼手龙的翅膀较窄,后肢

自由,尾巴高度缩小,长脖子长,头较大。在地面上,翼手龙四肢行走良好,姿势

直立,后足直立站立,翅膀手指向上折叠,用三指的“手”行走。化石轨迹显示,

至少有一些物种能够奔跑和涉水或游泳的[2]。

翼龙的毛发被称为小纤维,覆盖着它们的身体和翅膀的部分[3]。在生活中,翼

龙会有光滑或蓬松的皮毛,而不像鸟的羽毛。早期的说法认为,翼龙主要是冷血的

滑翔动物,像现代蜥蜴一样从环境中获得温暖,而不是燃烧卡路里。然而,后来的

研究表明,它们可能是温血动物(吸热动物)、活跃的动物。呼吸系统有有效的单

向“流动”呼吸,使用气囊极端挖空了他们的骨头。翼龙的成年体型很大,从非常

小的翼龙到已知最大的最大的飞行动物,包括羽翼龙和4,翼展至少达到9米

。结合恒温恒温,良好的氧气供应和强大肌肉使翼龙成为强大的飞行者。

目前,翼龙飞行的机制还没有被完全了解或建模。佐藤用现代鸟类进行了计算

,得出结论,翼龙不可能呆在[6]上。在《翼龙的姿势、运动和古生态学》一书中

,理论上认为它们能够飞行是由于白垩纪晚期[7]的富氧、致密的大气层。然而,

佐藤和《翼龙的姿势、运动和古生态学》的作者都是基于现在已经过时的翼龙类似

海鸟的理论,而且大小限制不适用于陆生翼龙,如翼龙和翼龙。此外,达伦·内什

得出结论,现在中生代和中生代之间的大气差异对于巨大的翼龙[8]并不需要。

另一个难以理解的问题是它们是如何起飞的。如果翼龙是冷血动物,目前还不

清楚体型巨大、新陈代谢效率低下的翼龙如何采取像鸟类一样的起飞策略,只利用

后肢产生推力。后来的研究表明,它们是温血动物,拥有强大的飞行肌肉,并利用

飞行肌肉行走作为四足动物[9]。朴茨茅斯大学的马克·威顿和约翰·霍普金斯大

学的迈克·哈比卜提出,翼龙使用了一种跳马机制来获得[10]飞行。它们有翅膀的

前肢的巨大力量将使它们能够轻松地起飞,使用[9]。一旦升空,翼龙可以达到高

达120 km/h的速度,并旅行数千公里的[10]。

你的团队被要求根据化石测量,开发出至少一只大型翼龙飞行过程的合理数学

模型,并回答以下问题。

1.对于你所选择的翼龙物种,估计一下它在正常飞行中的平均速度。

2.对于你所选择的翼龙种类,估计一下它在正常飞行中的翼瓣频率。

3.研究翼龙有多大;它们能像鸟一样在平地或水面上起飞吗?定量地解释这些

原因。

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