/sci/ - Science & Math

I have been thinking about general design of wings for rc-bird with more degrees of freedom compared to rc-birds you can find for sale these days.
It has taken me over 9 years of thinking about it every now and then to come up with this general design.

Each dof can be actuated independently by electric motor and each motor used for actuation of joints in wing + one extra motor are used for flapping motion. Also, wing structure becomes stronger in direction of flapping so it can be more lightweight compared to some other actuation designs.

I think this design can be scaled so that it can be used for human transportation. This was my main motivation but I would first design smaller rc-model that I would use to learn how to fly before I risk my life.
I have space and tools to build it as my family has transportation company that has its own facility for fixing trucks.

What areas of mathematics and engineering physics I need to master so that I can model this machine mathematically and optimize its shape and size? Any book recommendations?

My background is car mechanic school around 8 years ago and many years of electronics, programming, math and chemistry self-studies every now and then.
I am now studying mathematics at Khan Academy for spring entrance exams for chemical and mechanical engineering and mathematics.
I am more interested in mathematics and it would be my first choice as I have many interests that are all connected by it and I like to live inside my head.
If I get into university to study mathematics, I would need to study engineering by myself as I would only pic mathematics courses.
I am applying to study mechanical and chemical engineering because it is free and I get more money from the state if I am in school. If I don't like it much, I can change it later.

Thanks for help.

What areas of mathematics I need to study so that I can understand mathematical models of bird flight?