Musculoskeletal Dynamics Grant Schaffner

1. Kinematics of Mechanism: the study of motion without regard to forces That is about motion of the components and the basic geometry of the mechanism, and is not concerned with the forces which cause or affect the motion all the components of the mechanism are, in general considered rigid member 2. Kinetics or Dynamics of Mechanisms: the study of forces on the system in motion

The dynamics of many-particle systems is called statistical mechanics. The kinetic theory is a special aspect of the statistical mechanics of large number of particles. Suitable averages of the physical characteristics and motions of individual particles provide information about the macroscopic behavior of the system as a whole

7-1: The IS Relation in the open Economy 7-2: Equilibrium Output and the Trade Balance 7-3. Increases in Demand, Domestic or Foreign 7-4: Depreciation, the Trade Balance,and output 7-5: Looking at Dynamics: The J-Curve 7-6: Saving, Investment, and Trade Deficits

10. More on Production a. Derived Demand-Marshall's Laws b. Long Run/Short Run, LeChatelier, Dynamics C. Aggregating Supply d. Theory of the Firm, the Holdup Problem e. Agency Issues f. Application: The Coase Theorem

mu Xuu+ Xww-mg cos 000+ m(wi-qUo) Zuu+ Zww Ziw+ Zgq-mg sin+ Iyyq Muu+ Mww+ Mww+ Mq+ There is no roll/yaw motion, so=0. Control commands△x,△z,and△ MC have not yet been specified

Matrix Diagonalization Suppose a is diagonizable with independent eigenvectors use similarity transformations to diagonalize dynamics matrix

Note can develop good approximation of key aircraft motion(Phugoid) using simple balance between kinetic and potential energies. Consider an aircraft in steady, level flight with speed U and height ho. The motion is perturbed slightly so that

A pendulum is a rigid body suspended from a fixed point (hinge) which is offset with respect to the body's center of mass. If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum. Pendulums have played an important role in the history of dynamics. Galileo identified the pendulum as the first example of synchronous motion, which led to the first successful clock developed

In this lecture, we will particularize the conservation principles presented in the previous lecture to the case in which the system of particles considered is a 2D rigid body. Mass Moment of Inertia In the previous lecture, we established that the angular momentum of a system of particles relative to the center of mass, G, was