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The hydrodynamic forces acting on an undulating swimming fish consist of two components: a drag-based resistive force, and a reactive force originating from the necessary acceleration of an added mass of water. Lighthill’s elongated-body theory, based on potential flow, provides a framework for calculating this reactive force. By leveraging the high aspect ratio of most fish, the theory simplifies the problem into a series of independent two-dimensional slices of fluids along the fish’s body, which exchange momentum with the body and neighbouring slices. Using momentum conservation arguments, Lighthill’s theory predicts the total thrust generated by an undulating fish, based solely on the dimensions and kinematics of its caudal fin. However, the assumption of independent slices has led to the common misconception that the flow produced lacks a longitudinal component. In this paper, we revisit Lighthill’s theory, offering a modern reinterpretation using essential singularities of potential flows. We then extend it to predict the full three-dimensional flow field induced by the fish’s body motion. Our results compare favourably with numerical simulations of realistic fish geometries.
This chapter examines Shelley’s engagement with early-nineteenth-century science. It explores Shelley’s interest in chemistry at Oxford, his interest in contemporary developments in science (such as galvanism), and his reading of canonical and contemporary writers in science. Humphry Davy, the foremost man of science in Britain in the early nineteenth century, emerges as an important contemporary influence on Shelley; this chapter discusses the influence of Davy’s Elements of Chemical Philosophy (1812) and Elements of Agricultural Chemistry (1813) on Shelley’s writing, specifically in Bodleian MS Shelley adds. e. 6, Queen Mab (1813), and ‘The Cloud’ (1820).
While the federal government has adopted a policy of tribal self-determination, paternalism remains. The Moapa Band of Paiute Indians’ attempt to open a brothel is a prime example. Prostitution is legal in the surrounding state of Nevada; nevertheless, the Secretary of the Interior prohibited the tribe from doing so despite acknowledging it “is a profitable economic enterprise for non-Indians.” Though the federal government was supposed to ensure the Navajo Nation received a fair return on its natural resources, the United States Secretary of the Interior assisted in a private company in swindling the Navajo Nation. Similarly, the United States mismanaged Indian assets for more than a century. When Eloise Cobell sued the United States, the United States removed a federal judge who was ruling in favor of the Indian plaintiffs. The case was settled soon after. Additionally, the National Labor Relations Board imposes regulations on tribes that it does not impose on other governments. The United States also prohibits tribes from accessing the bonds other governments use to fund infrastructure projects.
This chapter focuses not on the possible content of a Bill of Rights, such as whether it should contain social and economic rights or only civil and political rights, but on the form any such Bill needs to take to be legitimate in a manner congruent with the moral norms of equal concern and respect underlying both rights and democracy. It explores four conceptions of Bills of Rights and the different ways they relate to democratic theory and practice. I start with the view of a Bill of Rights as distinct from normal legislation and that is ultimately the responsibility of the courts to defend. I distinguish between substantive and procedural accounts, in which the first focuses on upholding the rights necessary to ensure the outputs of democratic decisions reflect democratic norms whereas the second seeks to uphold the rights required for a due democratic process. I then turn to legislated rights and the role of Parliamentary Bills of Rights. Finally, I examine the role of democratic constitutional politics as a means for justifying and legitimising such rights instruments, be they upheld by legislatures or courts.
Territorial jurisdiction will require tribes to further develop their legal systems. People often assume tribal law is exotic, based upon ancient customs. While tribal law often includes customs, many legal systems do. Moreover, tribal law is often indistinguishable from state law. This is not assimilation; rather, this is to be expected. Many laws are universal because people generally want the same basic things. For example, theft and murder are prohibited everywhere. Likewise, tribes banned these offenses long before Europeans arrived on the continent. Though tribal law can deviate from standard Anglo-American law, different does not necessarily mean bad. Additionally, tribal courts usually resemble state and federal courts. Despite negative stereotypes, studies show tribal courts treat non-Indians fairly. Nevertheless, lack of funding – largely due to state taxation – inhibits tribes’ ability to develop bureaucracy. Lack of funding also prevents some tribes from publishing their laws. A possible solution to tribal institutional capacity is the creation of intertribal business courts. The intertribal nature of the tribunal will provide more resources to increase administrative capacity and help eliminate perceptions of bias.
Marx first calls for the actualization of philosophy in his earliest philosophical writings: the Notebooks on Epicurean Philosophy and Difference Between the Democritean and Epicurean Philosophy of Nature. This chapter examines those texts. It shows that Marx’s simultaneous praise of Epicurus for a great insight and condemnation for his shrinking from that insight relate to the problem of thought and reality, and that Marx’s identification of a ceaseless oscillation between the positions of a ‘liberal party’ and ‘positive philosophy’ already points the way beyond his own Young Hegelian context to the genuine actualization of philosophy.
When British troops entered Germany, they found ‘well dressed and well fed’ Germans, showing how much the Nazi state had plundered from occupied nations and camp inmates. Soon, however, prominent British opinion-shapers arrived at a new appreciation of German victimhood. Millions of ethnic German ‘expellees’ created a constituency of displaced persons whose basic needs had to be met. Central to this story is British publisher, humanitarian and activist Victor Gollancz, the force behind ‘Save Europe Now’ (SEN). Gollancz’s polemical interventions used ‘kaput’ shoes as emblems of German immiseration, evoking the footwear stripped from victims of Nazi genocide. While SEN encouraged Britons to send clothing and food parcels to Germans, British occupation authorities revised their understandings of former enemies and allies. The chapter concludes with the International Military Tribunal convened in Nuremberg to try leading Nazi war criminals in 1945–6. Noting the ‘deflation’ of Nazi leaders stripped of uniforms and insignia, British and US observers also remarked on poor Soviet apparel. Western attempts to kindle consumerist aspirations behind the Iron Curtain soon became prominent.
I introduce an important way to think about and construct a DCM: by implementing a yaw–pitch–roll sequence of rotations on a model aircraft. This does away with the widespread but rather involved method of describing the relative orientation of two axis sets by drawing them with a common origin. For this, we must distinguish the idea of a rotation in a sequence being about either a ‘space-fixed’ axis or a ‘carried-along’ axis. Users of these terms tend to fall into two groups, ‘active’ and ‘passive’. I state the ‘fundamental theorem of rotation sequences’, which does away with any need for the reader to stand in one group or the other. I also discuss the extraction of Euler angles from a DCM, and examine infinitesimal rotations. I discuss two methods of interpolating from an initial to a final orientation; one of these is used widely in computer graphics, but both methods must be discussed for the computer-graphics method to be understood. I end with a calculation of the position and attitude of a robot arm.