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Overview

How can geckoes walk on the ceiling and basilisk lizards run over water? What are the aerodynamic effects that enable small insects to fly? What are the relative merits of squids' jet-propelled swimming and fishes' tail-powered swimming? Why do horses change gait as they increase speed? What determines our own vertical leap? Recent technical advances have greatly increased researchers' ability to answer these questions with certainty and in detail.

This text provides an up-to-date overview of how animals run, walk, jump, crawl, swim, soar, hover, and fly. Excluding only the tiny creatures that use cilia, it covers all animals that power their movements with muscle—from roundworms to whales, clams to elephants, and gnats to albatrosses. The introduction sets out the general rules governing all modes of animal locomotion and considers the performance criteria—such as speed, endurance, and economy—that have shaped their selection. It introduces energetics and optimality as basic principles. The text then tackles each of the major modes by which animals move on land, in water, and through air. It explains the mechanisms involved and the physical and biological forces shaping those mechanisms, paying particular attention to energy costs.

Focusing on general principles but extensively discussing a wide variety of individual cases, this is a superb synthesis of current knowledge about animal locomotion. It will be enormously useful to advanced undergraduates, graduate students, and a range of professional biologists, physicists, and engineers.

Author Biography: R. McNeill Alexander is Emeritus Professor of Zoology at the University of Leeds and a Fellow of the Royal Society. He is the author of more than a dozen books, including Optima for Animals (Princeton), as well as the award-winning CD-ROM How Animals Move.

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Editorial Reviews

From the Publisher
"A valuable reference book written by a leader in the field."—Stephen Gatesy, Nature

"A remarkable volume that simply must be read by anyone contemplating any kind of work on, or in imitation of, muscle-driven motion. This is no ordinary summing up but rather a synthesis, an explication of principles—the title needs no disclaimer. . . . [O]ne should read it in short bouts separated by intervals of contemplation."—Steven Vogel, American Scientist

"This is an important work that will be appreciated by anyone interested in animal biomechanics. . . . Alexander is gifted in his ability to choose or create models that are sufficiently simple as to be understandable and tractable, but not so simple that they stray far from biological reality."—Robert Josephson, The Quarterly Review of Biology

"The book will be a godsend for any lecturer looking for a course book about animal locomotion, and many a naturalist will find that it sheds a flood of light on the reasons behind the endlessly surprising things that animals do. . . . [A] 'must have' for anyone who thinks in terms of physics about the way animals work."—C. J. Pennycuick, Trends in Ecology and Evolution

Nature
A valuable reference book written by a leader in the field.
— Stephen Gatesy
American Scientist
A remarkable volume that simply must be read by anyone contemplating any kind of work on, or in imitation of, muscle-driven motion. This is no ordinary summing up but rather a synthesis, an explication of principles—the title needs no disclaimer. . . . [O]ne should read it in short bouts separated by intervals of contemplation.
— Steven Vogel
The Quarterly Review of Biology
This is an important work that will be appreciated by anyone interested in animal biomechanics. . . . Alexander is gifted in his ability to choose or create models that are sufficiently simple as to be understandable and tractable, but not so simple that they stray far from biological reality.
— Robert Josephson
Trends in Ecology & Evolution
The book will be a godsend for any lecturer looking for a course book about animal locomotion, and many a naturalist will find that it sheds a flood of light on the reasons behind the endlessly surprising things that animals do. . . . [A] 'must have' for anyone who thinks in terms of physics about the way animals work.
— C. J. Pennycuick
Trends in Ecology and Evolution

The book will be a godsend for any lecturer looking for a course book about animal locomotion, and many a naturalist will find that it sheds a flood of light on the reasons behind the endlessly surprising things that animals do. . . . [A] 'must have' for anyone who thinks in terms of physics about the way animals work.
— C. J. Pennycuick
Nature - Stephen Gatesy
A valuable reference book written by a leader in the field.
American Scientist - Steven Vogel
A remarkable volume that simply must be read by anyone contemplating any kind of work on, or in imitation of, muscle-driven motion. This is no ordinary summing up but rather a synthesis, an explication of principles—the title needs no disclaimer. . . . [O]ne should read it in short bouts separated by intervals of contemplation.
The Quarterly Review of Biology - Robert Josephson
This is an important work that will be appreciated by anyone interested in animal biomechanics. . . . Alexander is gifted in his ability to choose or create models that are sufficiently simple as to be understandable and tractable, but not so simple that they stray far from biological reality.
Trends in Ecology and Evolution - C.J. Pennycuick
The book will be a godsend for any lecturer looking for a course book about animal locomotion, and many a naturalist will find that it sheds a flood of light on the reasons behind the endlessly surprising things that animals do. . . . [A] 'must have' for anyone who thinks in terms of physics about the way animals work.
Trends in Ecology and Evolution - C. J. Pennycuick
The book will be a godsend for any lecturer looking for a course book about animal locomotion, and many a naturalist will find that it sheds a flood of light on the reasons behind the endlessly surprising things that animals do. . . . [A] 'must have' for anyone who thinks in terms of physics about the way animals work.
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Product Details

  • ISBN-13: 9780691086781
  • Publisher: Princeton University Press
  • Publication date: 11/25/2002
  • Pages: 384
  • Product dimensions: 6.20 (w) x 9.30 (h) x 1.30 (d)

Meet the Author

R. McNeill Alexander is Emeritus Professor of Zoology at the University of Leeds and a Fellow of the Royal Society. He is the author of more than a dozen books, including "Optima for Animals" (Princeton), as well as the award-winning CD-ROM "How Animals Move".
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Read an Excerpt

Principles of Animal Locomotion


By R. McNeill Alexander

Princeton University Press

Princeton University Press
All right reserved.

ISBN: 0-691-12634-8


Chapter One

THE BEST WAY TO TRAVEL

THIS BOOK describes the movements of animals and of the structures such as legs, fins, or wings that they use for movement. It tries to explain the physical principles on which their movements depend. And it asks whether the particular structures and patterns of movement that we find in animals are better suited to their ways of life than possible alternatives. This chapter will, I hope, help us when we come to ask these questions about the merits of particular structures and movements.

The structures of animals and some of their patterns of movement (the ones that are inherited) have evolved. Other patterns of movement may be learned afresh by successive generations of animals, by trial and error. Evolution by natural selection, and learning by trial and error, both tend to make the animals and their behavior in some sense better. What, in this context, does "better" mean?

1.1. FITNESS

The most fundamental answer is that evolution favors structures and patterns of movement that increase fitness, and that the capacity for learning has evolved so that learning also can be expected to increase fitness. The fitness of an animal's complement of genes (its genotype) is the probability of the same group of genes being transmitted to subsequentgenerations. Unfortunately for the purposes of this book, it is not generally easy to measure or calculate the effect on fitness of, for example, a change in the length of an animal's legs or a modification of its gait. We can make more progress by looking at the effects of evolution in a less fundamental way.

Fitness depends largely on the number of offspring that animals produce, and on the proportion of those offspring that survive to breed. Thus, natural selection favors genotypes that increase fecundity or reduce mortality. This insight still seems rather remote from our discussions of locomotion. It seems helpful to ask at this stage, what aspects of an animal's performance in locomotion are most likely to affect fecundity and mortality, and so fitness? What qualities, in the context of locomotion, can natural selection be expected to favor? Some suggestions follow.

1.2. SPEED

For many animals, natural selection may tend to favor structures and patterns of movement that increase maximum speed. A faster-moving predator may be able to catch more prey, which may enable it to rear and feed more offspring. A faster moving prey animal may be better able to escape predators, and so may live longer. However, we should not assume that speed is important for all animals. For example, tortoises are herbivores, with no need for speed to catch prey. Their shells are sufficient protection against most predators, so they do not need speed to escape. It seems clear that maximum speed has had little importance in the evolution of tortoises, so we need not be surprised that tortoises are remarkably slow.

It is probably generally true that most animals spend very little of their time traveling at maximum speed. Lions (Panthera leo) are idle for most of the day, but their ability to run fast occasionally is vital to their hunting success. The antelopes and zebra on which they feed spend nearly all their time quietly grazing or traveling slowly, but depend on their ability to run fast in emergencies, to escape from lions and other predators. Ability to travel fast may be highly important to animals, although it may seldom be used.

1.3. ACCELERATION AND MANEUVERABILITY

Acceleration may be even more important than speed for predators such as lions, which stalk antelopes and then make a sudden dash from a short distance; and pike (Esox), which hide among vegetation and dash out to catch small fish that swim past. Acceleration must be correspondingly important for the prey. Suppose a predator dashes with constant acceleration [a.sub.pred], starting from rest at zero time, at a distance d from its prey. At time t its speed is [a.sub.pred]t, and it has traveled a distance 0.5[a.sub.pred][t.sup.2]. If the prey starts running at the same instant as the predator, with acceleration [sup.a]prey] it has traveled a distance 0.5[a.sub.prey][t.sup.2] at time t. If the predator's acceleration is greater than the prey's, and if the chase is short enough for neither animal to reach top speed, the predator catches the prey when by which time the predator has covered a distance [a.sub.pred] d/([a.sub.pred][a.sub.prey)]. If the predator has twice the acceleration of the prey, it catches it after covering a distance 2d; but if its acceleration is only 1.1 times that of the prey it has to run a distance 11d.

That analysis is grossly simplified. It assumes that both animals start moving simultaneously, and that both animals have constant acceleration throughout the chase. Elliott et al. (1977) filmed lions hunting gazelles (Gazella thomsoni), and used his films to calculate graphs of speed against time. These graphs curve and level off, showing that both predator and prey accelerated at decreasing rates, as they gained speed (Fig. 1.1). However, the analysis is sufficient to show that the ability of a predator to catch prey may depend more on its acceleration than on its maximum speed. Indeed, a predator with superior acceleration may be able to catch prey, even if its top speed is lower than that of the prey. Elliott found that the initial accelerations of the lions averaged 9.5 m/[s.sup.2], and those of the gazelles only 4.5 m/[s.sup.2.] He estimated that the speeds they would eventually have reached were 14 m/s for the lions, and a much faster 27 m/s for the gazelles. However, these estimates of top speed depended on extrapolation of his data, and may not be accurate.

The analysis also ignored the possibility that the prey might attempt to escape by swerving. Films of gazelles (Gazella thomsoni again) pursued by cheetah (Acinonyx jubatus) show the prey swerving when the predator is close behind. Children playing the game of tag (called tig in Britain) know that a well-timed swerve is a good escape strategy.

An animal traveling at speed v on a circular arc of radius r has an acceleration [v.sup.2]/r toward the center of the circle. Thus, swerving involves sideways acceleration. Suppose that a predator running at speed [v.sub.pred] is capable of swerving with radius [r.sub.pred], and a prey animal running with speed [v.sub.prey] swerves with radius [r.sub.prey]. The prey can escape, even if [v.sub.prey] is lower than [>v.sub.pred], if its sideways acceleration [v.sub.prey.sup.2]/[r.sub.prey] is greater than the predator's sideways acceleration [v.sub.pred.sup.2/r.sub.pred]. Howland (1974) pointed this out, and went on to show that, to take full advantage of its superior sideways acceleration, the prey must delay swerving until the predator is very close behind. This is illustrated in Fig. 1.2, which shows the paths of predator and prey. The predator is represented as traveling faster than the prey, but with larger radius. Time intervals are marked on the animals' paths. Each animal has the same speed and radius in both diagrams. The prey escapes if it swerves at the last possible moment (B), but if it swerves too soon the predator cuts off the corner and intercepts it (A).

1.4. ENDURANCE

Animals cannot maintain their top speeds indefinitely in a prolonged chase. Figure 1.3A shows the speeds at which human athletes have run races ranging from a 100-m sprint to a marathon, plotted against the time taken for the race. Figure 1.3B shows the maximum speeds maintained by trout (Salmo irideus) for different times. In each case speed falls as time and distance increase.

The graph for the fish (Fig. 1.3B) is plotted on ordinary linear coordinates. It shows, for example, that the 15-cm fish's maximum speed was 180 cm/s for one-second sprints, but fell, as time increased, toward an asymptote of about 40 cm/s. The graph for human running (Fig. 1.3A) would look very similar to the fish graph, if it had been plotted in the same way. However, it has been plotted on logarithmic coordinates, which have made it possible to display data for a much wider range of times. This graph shows not only that maximum speed declines markedly in the first 100 s of running time, but also that the decline continues over a period of several hours. The point for the 100-m race (triangle) is potentially misleading because sprinters are still accelerating over most of this distance. The remaining data, for races from 200 m to a marathon, form two straight lines meeting at an angle when plotted thus on logarithmic coordinates. This suggests that the decline in speed over short times (less than about 150 s) depends on a different phenomenon from the longer term decline in speed. We will find a likely explanation in Section 2.5.

Now suppose that a predator is chasing prey over a sufficient distance for us to ignore the acceleration period. We might, for example, be considering African hunting dogs (Lycaon), which chase antelopes over distances of several kilometers (van Lawick-Goodall and van Lawick-Goodall 1970). Assume that both animals are able to estimate the duration of the chase in advance, and choose the speeds that will take them furthest in that time. Though its sprinting speed may be less than that of the prey, the predator will eventually overtake the prey if its sustainable speed is greater than that of the prey. Less obviously, even though its sprinting speed and its maximum speed over long distances may be less than those of the prey, it may be able to catch the prey if it fatigues less quickly than the prey. Figure 1.3C is a schematic graph illustrating this possibility; notice how the lines cross, showing that there is a range of chase times for which the predator can travel faster than the prey.

1.5. ECONOMY OF ENERGY

Measurements of the oxygen consumption of many animals have been made, to find out how much energy they use in locomotion; the principal methods will be outlined in Section 5.3. Some striking differences have been observed. For example, Taylor et al. (1982) found that walking penguins (Pygoscelis) use energy about 60% faster than turkeys (Meleagris) of the same mass, walking at the same speed. In another comparison, this time of the energy cost of swimming at the surface of water, penguins (Eudyptula, in this case) performed much better; they used only 0.72 times as much energy as ducks (Anas) of equal mass, swimming at the same speed (Baudinette and Gill 1985). In a second comparison of swimmers, squid (Illex) used energy 1.75 times as fast as salmon (Onchorhynchus) of comparable mass, although they were swimming at only 0.6 times the speed of the fish (Webber and O'Dor 1986). Are these differences likely to be important to the animals?

Economy of energy can affect fitness in various ways, of which the most generally important is probably this: energy that is not used for locomotion is available for growth and reproduction. For example, birds rearing nestlings may have to spend all the daylight hours foraging for food, flying for much of the time. A substantial proportion of the food they collect has to be used to fuel flight, and so is not available to feed the nestlings. House martins (Delichon urbica) are small birds that feed on insects, which they catch on the wing. In field experiments in Scotland, Bryant and Westerterp (1980) set up nest boxes that were used by house martins. Trapdoors on the boxes enabled them to capture the birds, to make the injections and (a day or two later) collect the blood samples needed to measure their metabolic rates by the doubly labeled water technique, which is explained in Section 5.3. While they had young in the nest, the birds spent an average of 14 h per day off the nest, flying all the time, and their metabolic rates were 3.6 times the resting rate. For part of the time, the nestlings were temporarily fitted with collars that prevented them from swallowing, so that the experimenters could recover and weigh the mouthfuls of food that their parents gave them. The brood was found to be receiving food from each parent at a rate equivalent to 3.0 times the parent's resting metabolic rate, while the parents (as we have seen) were using energy at 3.6 times the resting rate for their own metabolism. A very large fraction of the energy that the parents were using, in excess of the resting rate, must have been used to power flight; and if they could have flown more economically they would have had more food to spare for the young. They might have been able to rear a larger brood, and so pass on more of their genes to the next generation.

As another example to show how economy of energy can affect fitness consider a typical fish, which, unlike the birds we have been considering, does not care for its young. The more eggs it lays (of given size and quality), the more offspring it will have and the more genes it is likely to contribute to successive generations; but the number of eggs it can produce is limited by its size. As a rough general rule, a mature female fish of mass m can be expected to produce a mass of 0.1 to 0.2m of eggs in the course of the season (Le Cren and Holdgate 1962). Other things being equal, the less energy it has had to use for locomotion in the course of its life, the more of its food energy intake will have been available for growth, the bigger it will have grown, and the more eggs it can lay. Alexander (1967) made a simple calculation to assess the likely effect of energy economy on fitness. I estimated that 20% of the energy content of the food eaten by a typical fish would be lost in feces and urine; 34% would be used for resting metabolism; 34% would be used to power swimming; and 12% would be available for growth and reproduction. If these estimates are realistic, three times as much energy is used for swimming as for growth and reproduction, so a 1% improvement in the efficiency of swimming can be expected to make 3% more energy available for growth and reproduction.

1.6. STABILITY

We have already noted that tortoises walk very slowly. The likely reason is that, if speed is unimportant, an animal can make do with very slow muscles. These can be very economical of energy, as will be explained in Section 2.5. Experiments with tortoise muscle have shown that it is remarkably economical (Woledge et al., 1985). We will see in Section 7.9 that stability is a problem for walking animals with very slow muscles, but that the problem can be alleviated by appropriate choice of gait. Natural selection seems to have optimized the gait of tortoises to obtain adequate stability with the slowest possible muscles.

1.7. COMPROMISES

The discussion so far may suggest that animals should evolve to be as fast as possible, to have the best possible acceleration, maneuverability and endurance, and to be as economical as possible of energy. However, these objectives are not always compatible. The example of tortoises has already shown us that an animal designed to walk as economically as possible cannot be fast. Similarly, no human athlete is a champion both in sprinting and in distance running, and an animal adapted to sprint as fast as possible would be unlikely to have good endurance. Sprinters and distance runners differ markedly in physique, the sprinters having well-developed muscles and the distance runners being less muscular, with bigger hearts capable of pumping a greater volume of blood at each stroke (Reilly et al., 1990). Evolution can be expected to favor compromises between the requirements of speed, endurance, economy, etc.

If we were to try to express the relationship between the locomotion of animals and their fitness in mathematical terms, we would have to conclude that fitness is a function of speed, acceleration, maneuverability, endurance, energy economy, and a great many other properties. It would not be at all obvious what the function should be, and if we were to try to assess the effect on fitness of some change (for example, longer legs or bigger thigh muscles) we would find ourselves doing elaborate and highly unreliable calculations. To make our discussions manageable, we must try to identify the properties that are most important, and concentrate on the effects that adaptations have on them. We can safely assume that racehorses have been selected for speed over distances of the order of a few kilometers, but for animals designed by natural selection, as distinct from selective breeding, the criteria for selection are generally less clear-cut.

(Continues...)



Excerpted from Principles of Animal Locomotion by R. McNeill Alexander Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

PREFACE ix

Chapter 1: The Best Way to Travel 1

1.1. Fitness 1
1.2. Speed 2
1.3. Acceleration and Maneuverability 2
1.4. Endurance 4
1.5. Economy of Energy 7
1.6. Stability 8
1.7. Compromises 9
1.8. Constraints 9
1.9. Optimization Theory 10
1.10. Gaits 12

Chapter 2: Muscle, the Motor 15

2.1. How Muscles Exert Force 15
2.2. Shortening and Lengthening Muscle 22
2.3. Power Output of Muscles 26
2.4. Pennation Patterns and Moment Arms 28
2.5. Power Consumption 31
2.6. Some Other Types of Muscle 34

Chapter 3: Energy Requirements for Locomotion 38

3.1. Kinetic Energy 38
3.2. Gravitational Potential Energy 39
3.3. Elastic Strain Energy 40
3.4. Work That Does Not Increase the Body's Mechanical Energy 42
3.5. Work Requirements 46
3.6. Oscillatory Movements 48

Chapter 4: Consequences of Size Differences 53

4.1. Geometric Similarity, Allometry, and the Pace of Life 53
4.2. Dynamic Similarity 58
4.3. Elastic Similarity and Stress Similarity 60

Chapter 5: Methods for the Study of Locomotion 68

5.1. Cinematography and Video Recording 68
5.2. Stationary Locomotion 70
5.3. Measurement of Energy Consumption 73
5.4. Observing Flow 74
5.5. Forces and Pressures 76
5.6. Recording Muscle Action 80
5.7. Recording Movement at a Distance 83
5.8. Properties of Materials 84

Chapter 6: Alternative Techniques for Locomotion on Land 86

6.1. Two-Anchor Crawling 86
6.2. Crawling by Peristalsis 88
6.3. Serpentine Crawling 90
6.4. Froglike Hopping 91
6.5. An Inelastic Kangaroo 93
6.6. A Minimal Model of Walking 95
6.7. The Synthetic Wheel 97
6.8. Walkers with Heavy Legs 98
6.9. Spring-Mass Models of Running 99
6.10. Comparisons 100

Chapter 7: Walking, Running, and Hopping 103

7.1. Speed 103
7.2. Gaits 109
7.3. Forces and Energy 114
7.4. Energy-Saving Springs 122
7.5. Internal Kinetic Energy 125
7.6. Metabolic Cost of Transport 128
7.7. Prediction of Optimal Gaits 133
7.8. Soft Ground, Hills, and Loads 136
7.9. Stability 139
7.10. Maneuverability 143

Chapter 8: Climbing and Jumping 146

8.1. Standing Jumps 146
8.2. Leg Design and Jumping Technique 150
8.3. Size and Jumping 153
8.4. Jumping from Branches 155
8.5. Climbing Vertical Surfaces and Walking on the Ceiling 159

Chapter 9: Crawling and Burrowing 166

9.1. Worms 166
9.2. Insect Larvae 170
9.3. Molluscs 171
9.4. Reptiles 176
9.5. Mammals 179

Chapter 10: Gliding and Soaring 181

10.1. Drag 181
10.2. Lift 183
10.3. Drag on Aerofoils 187
10.4. Gliding Performance 192
10.5. Stability 200
10.6. Soaring 201

Chapter 11: Hovering 209

11.1. Airflow around Hovering Animals 209
11.2. Lift Generation 213
11.3. Power for Hovering 221

Chapter 12: Powered Forward Flight 224

12.1. Aerodynamics of Flapping Flight 224
12.2. Power Requirements for Flight 228
12.3. Optimization of Flight 236

Chapter 13: Moving on the Surface of Water 240

13.1. Fisher Spiders 240
13.2. Basilisk Lizards 244
13.3. Surface Swimmers 246

Chapter 14: Swimming with Oars and Hydrofoils 249

14.1. Froude Efficiency 249
14.2. Drag-Powered Swimming 250
14.3. Swimming Powered by Lift on Limbs or Paired Fins 255
14.4. Swimming with Hydrofoil Tails 261
14.5. Porpoising 264

Chapter 15: Swimming by Undulation 266

15.1. Undulating Fishes 266
15.2. Muscle Activity in Undulating Fishes 277
15.3. Fins, Tails, and Gaits 282
15.4. Undulating Worms 284

Chapter 16: Swimming by Jet Propulsion 288

16.1. Efficiency of Jet Propulsion 288
16.2. Elastic Mechanisms in Jet Propulsion 296

Chapter 17: Buoyancy 301

17.1. Buoyancy Organs 301
17.2. Swimming by Dense Animals 303
17.3. Energetics of Buoyancy 307
17.4. Buoyancy and Lifestyle 311

Chapter 18: Aids to Human Locomotion 316

18.1. Shoes 316
18.2. Bicycles 318
18.3. Scuba 321
18.4. Boats 322
18.5. Aircraft without Engines 324

Chapter 19: Epilogue 327

19.1. Metabolic Cost of Transport 327
19.2. Speeds 328
19.3. Gaits 330
19.4. Elastic Mechanisms 331
19.5. Priorities for Further Research 331

REFERENCES 333
INDEX 367

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"The lack of a comprehensive text has been the source of substantial frustration to those who teach courses in animal locomotion. It is a great pleasure, then, to see the publication of this book. It is poised to become an instant classic and will undoubtedly serve as the central source of distilled wisdom on the subject for many years to come."—Mark Denny, Stanford University

"One of the major gaps in the literature of biomechanics is a general textbook on animal locomotion, and it is difficult to imagine anyone better suited to write one than Alexander. He is a leading researcher, and his books always convey the interest and excitement of his field to a broad audience. I look forward to using this book in my own classes."—Robert Dudley, University of California, Berkeley

"This is unique, important, and useful synthesis that brings together an analysis of locomotion on land, in water, and in the air. There is no other contemporary book on animal locomotion that is as broad in scope, and I expect that it will become a classic in the field."—Thomas J. Roberts, Oregon State University

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