Development of a Dynamic Virtual Reality Model of the Inner Ear Sensory System as a Learning and Demonstrating Tool

Table 3

Expressions of the head angular velocity and of the acceleration of the origin of R₃.

	Case  1	Case  2	Case  3
𝜔2/0	𝜔2/0=(𝛾̇+𝛿̇)𝐙2	𝜔2/0=−𝛿̇sin𝛽𝐗2+𝛽̇𝐘2+𝛿̇cos𝛽𝐙2	𝜔2/0=𝛼̇𝐗2+𝛿̇sin𝛼𝐘2+𝛿̇cos𝛼𝐙2
𝐀𝐁,2/0	𝐀𝐁,2/0=𝐑2|^−̈̈−^̇𝛿^𝛿𝐝−𝛾𝐝2̇𝛾𝐝−^2̇𝛾^̇0𝐝−2𝛿𝐝	𝐀𝐁,2/0=𝐑2|^−̈−^̇𝛿^𝛿𝐝cos𝛽2𝐝−̈𝛿𝐝sin𝛽	𝐀𝐁,2/0=𝐑2|^−̈̇𝛼̇−^̇𝛿^𝛿𝐝cos𝛼+2𝛿𝐝sin𝛼2𝐝(cos𝛼)^2−^̇𝛼^2𝐝̇𝛿2̈𝛼𝐝cos𝛼sin𝛼+𝐝