# Mathematical aspects of the study of dinosaur locomotion

I'm interested in getting a better understanding of dinosaur locomotion. Therefore, I am looking for a book that will cover various mathematical aspects and discuss various mathematical tools for studying dinosaur locomotion. I do not have a basic biological education with a specialization in paleontology. However, I am proficient in some computer algebra packages and I enjoy learning applied mathematics.

Can anyone suggest good names that give a good basic and systematic idea of ​​the problem described above (with examples of the use of computer algebra packages if possible)?

I have tried searching for suitable sources. I came across mostly articles on a narrow specialized issue. And I would like the first sources to give me a general idea of ​​​​the general methodology, so to speak.

The object of study is clear: the musculoskeletal system of dinosaurs. Subject of study: mass-dimensional properties of dinosaurs, kinematics and dynamics of their movement. I have not fully formed in my head the methods that are used for research. It is clear that these are elements of mechanics and statistical analysis. Well, that's all I know today.

Specialized articles I found:

1. William Irvin Sellers, Lee Margetts, Rodolfo Aníbal Coria, Phillip Lars Manning. March of the Titans: The Locomotor Capabilities of Sauropod Dinosaurs

2. Bohun, Sean. Mathematical model of the mechanics and dynamics of the tails in dinosaurs.

Update March 23, 2023:

After a necessary pause, I returned to the study of this topic. An image formed in my head of how the movement of dinosaurs is studied. But some things need clarification. For example, in article 1 that I cited here ("March of the Titans") there is a figure 4. I am attaching a screenshot here.

In the figure, everything is more or less clear to me, except for these red cylinders. The article (in the section Muscle and Joint Locations) describes at length what it is. But neither specific methods nor principles are given.

So my new question is about this. If respected experts will help me figure it out, I will be very happy and grateful.

• What research have you done on this already? Have you looked for literature reviews or even primary literature, such as on Google Scholar? That may be a much better (and certainly more up-to-date) resource than a book. For example, look through the results of this search. Oct 30, 2022 at 21:04
• @MattDMo see my edit, please
– dtn
Oct 31, 2022 at 4:20
• can you edit your question to include some of the specialized articles you found? I'm guessing that you won't find books on dinosaur locomotion/kinematics specifically. However, if you search for/find articles on models for animal locomotion/kinematics more generally, that will probably give you most of the background you need to understand more specialized studies. Nov 2, 2022 at 16:34
• The cylinders will be approximations of muscle groups and/or tendon/ligaments.
– bob1
Mar 23 at 20:00
• @dtn Position will be based on anatomical clues - you can see on bones where soft tissue attaches and the size correlates with strength/stressors put on the muscle or bone attached. I don't know much more than that though as I have very little anatomy training.
– bob1
Mar 24 at 4:31

At OP's request:

Disclaimer: I don't have any full answers to this question or any training in anatomy beyond the basics from undergrad many years ago, so if any of this is outright wrong, feel free to correct me and either comment so that I can fix it or fix it yourself.

In the update in March 2023; OP asked what is the purpose of the cylinders and how are they determined?

The rods are approximations of muscle groups and their attachment points on the bones. If you look closely at the diagram you will see small bumps or lumps in the bone structure. These lumps are called by various names in anatomy, depending on who named them, how big they are and a range of other factors. These names include things like Processes, Tubercules, and Eminences. These bits indicate the attachment points of tendons (I remember it by: tendons are tenderer and join muscle to bone.) and ligaments (bone to bone) to the bones. There are also other anatomical markings that indicate the attachment points, but I don't know the names of them.

One might presume that, based on what we know of the anatomy of similar animals in the current day, we could use that knowledge to predict what the muscles and joints of dinosaurs look like, and how they behave. Of course, many dinosaurs were much larger than modern animals, but this is not always the case; the smallest dinosaurs that we know of are about the size of a hummingbird1, so this might not be an insuperable problem. In addition, the bones of many dinosaurs are so similar in structure to modern animal bones, that, even with a basic knowledge of anatomy, you can easily identify the major bones such as femurs and vertebrae, no matter how large (or small) they are. This means we can make some extrapolations from current animals to dinosaurs as to how the joints and muscles worked and where they were placed.

As to how the models of the muscles work, I have no idea. I do know that muscle strength doesn't scale with size necessarily, but does with cross-section2, but beyond that I have no knowledge of what this might mean for an anatomical model and how to apply it.

Refs:

1: Xing, L., O’Connor, J.K., Schmitz, L. et al. Hummingbird-sized dinosaur from the Cretaceous period of Myanmar. Nature 579, 245–249 (2020). https://doi.org/10.1038/s41586-020-2068-4

2: Jones EJ, Bishop PA, Woods AK, Green JM. Cross-sectional area and muscular strength: a brief review. Sports Med. 2008;38(12):987-94. doi: 10.2165/00007256-200838120-00003. PMID: 19026016.